bug366, discussion (missed optimization)

Time bar (total: 2.4s)

start0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

analyze30.0ms (1.3%)

Memory
26.6MiB live, 26.6MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
0%0%99.9%0.1%0%0%0%1
0%0%99.9%0.1%0%0%0%2
0%0%99.9%0.1%0%0%0%3
0%0%99.9%0.1%0%0%0%4
30.8%25%56.2%0.1%0%18.7%0%5
32%25%53.1%0.1%0%21.9%0%6
55.8%37.5%29.7%0.1%0%32.8%0%7
57.8%37.5%27.3%0.1%0%35.1%0%8
74.2%43.7%15.2%0.1%0%41%0%9
75.9%43.7%13.9%0.1%0%42.3%0%10
85.9%46.8%7.7%0.1%0%45.4%0%11
87%46.8%7%0.1%0%46.1%0%12
Compiler

Compiled 10 to 8 computations (20% saved)

sample733.0ms (30.5%)

Memory
-0.1MiB live, 618.2MiB allocated; 144ms collecting garbage
Samples
440.0ms8 256×0valid
41.0ms625×0invalid
Precisions
Click to see histograms. Total time spent on operations: 255.0ms
ival-mult: 151.0ms (59.3% of total)
ival-sqrt: 59.0ms (23.2% of total)
ival-sub: 39.0ms (15.3% of total)
adjust: 3.0ms (1.2% of total)
ival-assert: 3.0ms (1.2% of total)
Bogosity

explain77.0ms (3.2%)

Memory
-29.4MiB live, 70.0MiB allocated; 10ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
1270-2(-7.622345408597024e-157 -4.588494764601322e-253)(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
210-0-(-.f64 (*.f64 a a) (*.f64 b b))
00-0-(*.f64 a a)
00-0-a
00-0-b
00-0-(*.f64 b b)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
sqrt.f64(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))oflow-rescue1150
↳(*.f64 b b)overflow21
↳(-.f64 (*.f64 a a) (*.f64 b b))overflow115
↳(*.f64 a a)overflow115
-.f64(-.f64 (*.f64 a a) (*.f64 b b))nan-rescue210
↳(*.f64 a a)overflow115
↳(*.f64 b b)overflow21
sqrt.f64(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))uflow-rescue100
↳(*.f64 b b)underflow111
↳(-.f64 (*.f64 a a) (*.f64 b b))underflow10
↳(*.f64 a a)underflow10
Confusion
Predicted +Predicted -
+1252
-0129
Precision
1.0
Recall
0.984251968503937
Confusion?
Predicted +Predicted MaybePredicted -
+12502
-00129
Precision?
1.0
Recall?
0.984251968503937
Freqs
test
numberfreq
0131
1104
221
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
28.0ms512×0valid
Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 7.0ms (47% of total)
ival-sub: 3.0ms (20.1% of total)
ival-sqrt: 3.0ms (20.1% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess114.0ms (4.7%)

Memory
7.3MiB live, 53.6MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01850
15550
221450
334450
487550
5183950
6301750
7335950
8343750
9343750
10363350
068
0108
1238
2838
32258
44058
58368
613878
720718
828968
932068
1032688
1132688
1233468
033468
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
Outputs
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
Symmetry

(abs a)

(abs b)

Compiler

Compiled 8 to 6 computations (25% saved)

eval0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶53.6%
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
Compiler

Compiled 8 to 6 computations (25% saved)

simplify67.0ms (2.8%)

Memory
-12.2MiB live, 34.2MiB allocated; 2ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 b b)
cost-diff0
(*.f64 a a)
cost-diff0
(-.f64 (*.f64 a a) (*.f64 b b))
cost-diff0
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0623
01023
12323
28323
322523
440523
583623
6138723
7207123
8289623
9320623
10326823
11326823
12334623
0334623
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b
Outputs
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 a a)
a
(*.f64 b b)
b

localize20.0ms (0.8%)

Memory
16.0MiB live, 16.0MiB allocated; 0ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 b b)
accuracy0.0
(*.f64 a a)
accuracy4.191406250000001
(-.f64 (*.f64 a a) (*.f64 b b))
accuracy29.25763327696742
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
Samples
15.0ms256×0valid
Compiler

Compiled 25 to 8 computations (68% saved)

Precisions
Click to see histograms. Total time spent on operations: 7.0ms
ival-mult: 4.0ms (53.8% of total)
ival-sqrt: 2.0ms (26.9% of total)
ival-sub: 1.0ms (13.4% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.3%)

Memory
5.4MiB live, 5.4MiB allocated; 0ms collecting garbage
Counts
4 → 30
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (- (pow a 2) (pow b 2))))
#s(approx (* a a) #s(hole binary64 (pow a 2)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (pow a 2)))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (+ (* -1 (pow b 2)) (pow a 2))))
#s(approx (* b b) #s(hole binary64 (pow b 2)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
a
@0
((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms
a
@inf
((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms
b
@inf
((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms
b
@0
((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))
1.0ms
a
@-inf
((sqrt (- (* a a) (* b b))) (- (* a a) (* b b)) (* a a) (* b b))

simplify125.0ms (5.2%)

Memory
-11.3MiB live, 83.8MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0153799
1406798
21910787
08751707
Stop Event
1×iter limit
1×node limit
Counts
30 → 30
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (- (pow a 2) (pow b 2))))
#s(approx (* a a) #s(hole binary64 (pow a 2)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (pow a 2)))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (+ (* -1 (pow b 2)) (pow a 2))))
#s(approx (* b b) #s(hole binary64 (pow b 2)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
Outputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) a) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64))) (*.f64 a a) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (*.f64 a a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (*.f64 (/.f64 a (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (/.f64 a (pow.f64 b #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64)))) (*.f64 a a) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (*.f64 a a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (- (pow a 2) (pow b 2))))
#s(approx (- (* a a) (* b b)) (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* a a) #s(hole binary64 (pow a 2)))
#s(approx (* a a) (*.f64 a a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) a)
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (*.f64 b b) a) (/.f64 (*.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 a #s(literal 4 binary64)))) a a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (/.f64 (*.f64 b b) a) #s(literal 1 binary64)))) a))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (pow a 2)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))))
#s(approx (- (* a a) (* b b)) (*.f64 (*.f64 (neg.f64 a) a) (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) (neg.f64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (*.f64 b b) a) #s(literal -1 binary64)) a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (*.f64 b b) a) #s(literal -1 binary64))) a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal 1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) a) (/.f64 (*.f64 b b) a) #s(literal -1 binary64))) (/.f64 (*.f64 (pow.f64 b #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 a #s(literal 6 binary64)))) a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (*.f64 b b) a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64))) (*.f64 b b) (/.f64 #s(literal -1/2 binary64) a)) (*.f64 b b) a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (fma.f64 (*.f64 b (/.f64 b (pow.f64 a #s(literal 5 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64)))) (*.f64 b b) (/.f64 #s(literal -1/2 binary64) a)) (*.f64 b b) a))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (+ (* -1 (pow b 2)) (pow a 2))))
#s(approx (- (* a a) (* b b)) (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* b b) #s(hole binary64 (pow b 2)))
#s(approx (* b b) (*.f64 b b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (fma.f64 (*.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 a b) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 (*.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 a b) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (/.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 (*.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 a b) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))) b))
#s(approx (- (* a a) (* b b)) #s(hole binary64 (* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))))
#s(approx (- (* a a) (* b b)) (*.f64 (fma.f64 (/.f64 a b) (/.f64 a b) #s(literal -1 binary64)) (*.f64 b b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (neg.f64 b) (fma.f64 (*.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 a b) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (neg.f64 b) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 (*.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 a b) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (neg.f64 b) (fma.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 b #s(literal 6 binary64))) (/.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (fma.f64 (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 (*.f64 (/.f64 a (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 a b) b)) #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))

rewrite43.0ms (1.8%)

Memory
26.9MiB live, 26.9MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0621
01021
14121
035221
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
4 → 81
Calls
Call 1
Inputs
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
(*.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(*.f64 (pow.f64 (+.f64 b a) #s(literal 1/2 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (hypot.f64 b a))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(exp.f64 (*.f64 (log.f64 (*.f64 (-.f64 a b) (+.f64 b a))) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (neg.f64 a) (neg.f64 b)) (-.f64 (neg.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (neg.f64 a) (fabs.f64 b)) (-.f64 (neg.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (neg.f64 a) b) (-.f64 (neg.f64 a) b))
(*.f64 (+.f64 (fabs.f64 a) (neg.f64 b)) (-.f64 (fabs.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) (fabs.f64 b)) (-.f64 (fabs.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) b) (-.f64 (fabs.f64 a) b))
(*.f64 (+.f64 a (neg.f64 b)) (-.f64 a (neg.f64 b)))
(*.f64 (+.f64 a (fabs.f64 b)) (-.f64 a (fabs.f64 b)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(/.f64 (+.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 b) b) #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (*.f64 a a) (*.f64 (neg.f64 b) b)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (neg.f64 (fma.f64 b b (*.f64 a a))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (neg.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 b (neg.f64 b) (*.f64 a a))
(fma.f64 a a (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 a a (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) b))
(-.f64 (*.f64 a a) (*.f64 b b))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(*.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)))
(*.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)))
(*.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(*.f64 a a)
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 (fabs.f64 a) #s(literal 2 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 a) a))
(neg.f64 (*.f64 a (neg.f64 a)))
(fabs.f64 (*.f64 a a))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(*.f64 (pow.f64 b #s(literal 1 binary64)) (pow.f64 b #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 (fabs.f64 b)) (neg.f64 (fabs.f64 b)))
(*.f64 (fabs.f64 (fabs.f64 b)) (fabs.f64 (fabs.f64 b)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 (fabs.f64 b) (fabs.f64 b))
(*.f64 b b)
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (fabs.f64 b) #s(literal 2 binary64))
(pow.f64 b #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 b) b))
(fabs.f64 (*.f64 b b))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))

eval16.0ms (0.7%)

Memory
-30.9MiB live, 15.2MiB allocated; 3ms collecting garbage
Compiler

Compiled 1 723 to 381 computations (77.9% saved)

prune3.0ms (0.1%)

Memory
6.5MiB live, 6.5MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1064110
Fresh000
Picked101
Done000
Total1074111
Accuracy
100.0%
Counts
111 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶99.3%
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
▶54.3%
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
▶99.2%
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
▶98.6%
#s(approx (sqrt (- (* a a) (* b b))) a)
Compiler

Compiled 48 to 32 computations (33.3% saved)

simplify121.0ms (5%)

Memory
-4.7MiB live, 90.5MiB allocated; 11ms collecting garbage
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
cost-diff0
(sqrt.f64 (-.f64 a b))
cost-diff0
(+.f64 b a)
cost-diff0
(sqrt.f64 (+.f64 b a))
cost-diff0
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
cost-diff0
(+.f64 b a)
cost-diff0
(-.f64 a b)
cost-diff0
(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff0
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
cost-diff0
(*.f64 (/.f64 b a) (/.f64 b a))
cost-diff0
(*.f64 a #s(literal -1/2 binary64))
cost-diff0
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
cost-diff4
(fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a)
cost-diff0
#s(approx (sqrt (- (* a a) (* b b))) a)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
020108
032108
167108
2206108
3656108
41838102
54142102
66537102
08398100
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
(fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a)
(*.f64 a #s(literal -1/2 binary64))
a
#s(literal -1/2 binary64)
(*.f64 (/.f64 b a) (/.f64 b a))
(/.f64 b a)
b
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (+.f64 b a))
(+.f64 b a)
b
a
(sqrt.f64 (-.f64 a b))
(-.f64 a b)
Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)
a
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 #s(literal -1/2 binary64) a) (*.f64 b b) a))
(fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a)
(fma.f64 (/.f64 #s(literal -1/2 binary64) a) (*.f64 b b) a)
(*.f64 a #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) a)
a
#s(literal -1/2 binary64)
(*.f64 (/.f64 b a) (/.f64 b a))
(*.f64 (/.f64 (/.f64 b a) a) b)
(/.f64 b a)
b
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(sqrt.f64 (+.f64 b a))
(+.f64 b a)
b
a
(sqrt.f64 (-.f64 a b))
(-.f64 a b)

localize48.0ms (2%)

Memory
-4.2MiB live, 41.0MiB allocated; 5ms collecting garbage
Localize:

Found 13 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(+.f64 b a)
accuracy0.00390625
(sqrt.f64 (-.f64 a b))
accuracy0.00390625
(sqrt.f64 (+.f64 b a))
accuracy0.4453125
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
accuracy0.0
(-.f64 a b)
accuracy0.0
(+.f64 b a)
accuracy0.0
(*.f64 (-.f64 a b) (+.f64 b a))
accuracy29.25763327696742
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
accuracy0.0
(/.f64 b a)
accuracy0.0
(*.f64 a #s(literal -1/2 binary64))
accuracy0.21712875976844204
(*.f64 (/.f64 b a) (/.f64 b a))
accuracy0.518177132210616
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
accuracy0.9022517740528054
#s(approx (sqrt (- (* a a) (* b b))) a)
Samples
34.0ms256×0valid
Compiler

Compiled 96 to 21 computations (78.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 23.0ms
ival-mult: 10.0ms (43.5% of total)
ival-sqrt: 6.0ms (26.1% of total)
ival-div: 2.0ms (8.7% of total)
ival-add: 2.0ms (8.7% of total)
ival-sub: 2.0ms (8.7% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series29.0ms (1.2%)

Memory
36.0MiB live, 36.0MiB allocated; 0ms collecting garbage
Counts
13 → 148
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
(fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
(*.f64 a #s(literal -1/2 binary64))
(*.f64 (/.f64 b a) (/.f64 b a))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (+.f64 b a))
(sqrt.f64 (-.f64 a b))
(/.f64 b a)
Outputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (* a -1/2) #s(hole binary64 (* -1/2 a)))
#s(approx (* (/ b a) (/ b a)) #s(hole binary64 (/ (pow b 2) (pow a 2))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (+ b a) #s(hole binary64 b))
#s(approx (+ b a) #s(hole binary64 (+ a b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* (sqrt b) (sqrt -1))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))))
#s(approx (/ b a) #s(hole binary64 (/ b a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 a))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 a))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (pow a 2)))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))))
#s(approx (- a b) #s(hole binary64 a))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (+ b a) #s(hole binary64 a))
#s(approx (+ b a) #s(hole binary64 (* a (+ 1 (/ b a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))))
#s(approx (- a b) #s(hole binary64 (* -1 (* a (- (/ b a) 1)))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* a (- (* -1 (/ b a)) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* b (+ a (* -1 a))) (pow a 2))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))))
#s(approx (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))))
#s(approx (- a b) #s(hole binary64 (* b (- (/ a b) 1))))
#s(approx (+ b a) #s(hole binary64 (* b (+ 1 (/ a b)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt b) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))))
Calls

6 calls:

TimeVariablePointExpression
5.0ms
b
@-inf
((sqrt (- (* a a) (* b b))) (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (sqrt (- (* a a) (* b b))) (* a -1/2) (* (/ b a) (/ b a)) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (sqrt (- a b)) (/ b a))
5.0ms
b
@inf
((sqrt (- (* a a) (* b b))) (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (sqrt (- (* a a) (* b b))) (* a -1/2) (* (/ b a) (/ b a)) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (sqrt (- a b)) (/ b a))
5.0ms
a
@inf
((sqrt (- (* a a) (* b b))) (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (sqrt (- (* a a) (* b b))) (* a -1/2) (* (/ b a) (/ b a)) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (sqrt (- a b)) (/ b a))
4.0ms
a
@-inf
((sqrt (- (* a a) (* b b))) (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (sqrt (- (* a a) (* b b))) (* a -1/2) (* (/ b a) (/ b a)) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (sqrt (- a b)) (/ b a))
4.0ms
a
@0
((sqrt (- (* a a) (* b b))) (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (sqrt (- (* a a) (* b b))) (* a -1/2) (* (/ b a) (/ b a)) (sqrt (* (- a b) (+ b a))) (* (- a b) (+ b a)) (- a b) (+ b a) (* (sqrt (+ b a)) (sqrt (- a b))) (sqrt (+ b a)) (sqrt (- a b)) (/ b a))

simplify139.0ms (5.8%)

Memory
5.4MiB live, 94.8MiB allocated; 9ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07314420
122643548
095193311
Stop Event
1×iter limit
1×node limit
Counts
148 → 148
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (* a -1/2) #s(hole binary64 (* -1/2 a)))
#s(approx (* (/ b a) (/ b a)) #s(hole binary64 (/ (pow b 2) (pow a 2))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (+ b a) #s(hole binary64 b))
#s(approx (+ b a) #s(hole binary64 (+ a b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* (sqrt b) (sqrt -1))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))))
#s(approx (/ b a) #s(hole binary64 (/ b a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 a))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6)))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 a))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 a))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (pow a 2)))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))))
#s(approx (- a b) #s(hole binary64 a))
#s(approx (- a b) #s(hole binary64 (* a (+ 1 (* -1 (/ b a))))))
#s(approx (+ b a) #s(hole binary64 a))
#s(approx (+ b a) #s(hole binary64 (* a (+ 1 (/ b a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3))) (* 1/2 (* (sqrt (/ 1 (pow a 3))) b))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (sqrt a)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (* -1/2 (* (sqrt (/ 1 (pow a 3))) b))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* a (+ (sqrt (/ 1 a)) (+ (* -1/2 (* (sqrt (/ 1 (pow a 3))) b)) (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (pow b 2))) (* -1/16 (* (sqrt (/ 1 (pow a 7))) (pow b 3)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 a)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (* -1/8 (/ (pow b 4) (pow a 4)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* a (+ 1 (+ (* -1/2 (/ (pow b 2) (pow a 2))) (+ (* -1/8 (/ (pow b 4) (pow a 4))) (* -1/16 (/ (pow b 6) (pow a 6))))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))))
#s(approx (- a b) #s(hole binary64 (* -1 (* a (- (/ b a) 1)))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* a (- (* -1 (/ b a)) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (/ (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (/ (pow b 3) (pow (sqrt -1) 4)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) b)) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt a) (pow (sqrt -1) 2)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* a (+ (* -1/8 (* (sqrt (/ 1 (pow a 5))) (* (pow b 2) (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow a 7))) (* (pow b 3) (pow (sqrt -1) 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow a 3))) (* b (pow (sqrt -1) 2)))) (* (sqrt (/ 1 a)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* -1/8 (/ (pow b 2) (pow a 3))) (* 1/2 (/ 1 a)))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ a (* (pow b 2) (- (* (pow b 2) (- (* -1/16 (/ (pow b 2) (pow a 5))) (* 1/8 (/ 1 (pow a 3))))) (* 1/2 (/ 1 a)))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* b (+ a (* -1 a))) (pow a 2))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))))
#s(approx (- a b) #s(hole binary64 (+ a (* -1 b))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* 1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)) (* 1/2 (sqrt (/ 1 a))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt a) (* b (+ (* 1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* 1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* -1/2 (* (sqrt (/ 1 a)) b)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* -1/8 (* (sqrt (/ 1 (pow a 3))) b)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (sqrt a) (* b (+ (* -1/2 (sqrt (/ 1 a))) (* b (+ (* -1/8 (sqrt (/ 1 (pow a 3)))) (* -1/16 (* (sqrt (/ 1 (pow a 5))) b)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))))
#s(approx (- a b) #s(hole binary64 (* b (- (/ a b) 1))))
#s(approx (+ b a) #s(hole binary64 (* b (+ 1 (/ a b)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3))))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* b (+ (sqrt (/ 1 b)) (+ (* -1/8 (* (pow a 2) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (pow a 3) (sqrt (/ 1 (pow b 7))))) (* 1/2 (* a (sqrt (/ 1 (pow b 3)))))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1))))))))))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (+ (* -1/8 (/ (pow a 4) (* (pow b 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow a 6) (* (pow b 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow a 2) (* (pow b 2) (sqrt -1)))))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))
#s(approx (+ b a) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt b) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))))
Outputs
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* 1/2 (/ (pow a 2) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 a a) b) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* -1/8 (/ (pow a 2) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (/.f64 (*.f64 a a) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (*.f64 a a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (- (* a a) (* b b))) #s(hole binary64 (+ (* b (sqrt -1)) (* (pow a 2) (+ (* (pow a 2) (- (* 1/16 (/ (pow a 2) (* (pow b 5) (pow (sqrt -1) 5)))) (* 1/8 (/ 1 (* (pow b 3) (pow (sqrt -1) 3)))))) (* 1/2 (/ 1 (* b (sqrt -1)))))))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 (-.f64 (/.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) a) a) (*.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)) (pow.f64 b #s(literal 5 binary64)))) (/.f64 #s(literal 1/8 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64)))) (*.f64 a a) (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) (*.f64 a a) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (*.f64 (/.f64 (*.f64 b b) a) #s(literal -1/2 binary64)))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (+ (* (* a -1/2) (* (/ b a) (/ b a))) a) (/.f64 (fma.f64 (*.f64 b b) #s(literal -1/2 binary64) (*.f64 a a)) a))
#s(approx (* a -1/2) #s(hole binary64 (* -1/2 a)))
#s(approx (* a -1/2) (*.f64 #s(literal -1/2 binary64) a))
#s(approx (* (/ b a) (/ b a)) #s(hole binary64 (/ (pow b 2) (pow a 2))))
#s(approx (* (/ b a) (/ b a)) (*.f64 (/.f64 b a) (/.f64 b a)))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (fma.f64 a (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* -1 (pow b 2))))
#s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))))
#s(approx (* (- a b) (+ b a)) (fma.f64 (neg.f64 b) b #s(literal 0 binary64)))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))))
#s(approx (* (- a b) (+ b a)) (*.f64 (+.f64 b a) (-.f64 a b)))
#s(approx (- a b) #s(hole binary64 (* -1 b)))
#s(approx (- a b) (neg.f64 b))
#s(approx (- a b) #s(hole binary64 (- a b)))
#s(approx (- a b) (-.f64 a b))
#s(approx (+ b a) #s(hole binary64 b))
#s(approx (+ b a) b)
#s(approx (+ b a) #s(hole binary64 (+ a b)))
#s(approx (+ b a) (+.f64 b a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 a (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (fma.f64 a (/.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (sqrt b)))
#s(approx (sqrt (+ b a)) (sqrt.f64 b))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* 1/2 (* a (sqrt (/ 1 b)))))))
#s(approx (sqrt (+ b a)) (fma.f64 (*.f64 a #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* -1/8 (* a (sqrt (/ 1 (pow b 3))))) (* 1/2 (sqrt (/ 1 b))))))))
#s(approx (sqrt (+ b a)) (fma.f64 (fma.f64 (*.f64 a #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal 1/2 binary64))) a (sqrt.f64 b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (+ (sqrt b) (* a (+ (* 1/2 (sqrt (/ 1 b))) (* a (+ (* -1/8 (sqrt (/ 1 (pow b 3)))) (* 1/16 (* a (sqrt (/ 1 (pow b 5))))))))))))
#s(approx (sqrt (+ b a)) (fma.f64 (fma.f64 (fma.f64 (*.f64 #s(literal 1/16 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) #s(literal -1/8 binary64))) a (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) #s(literal 1/2 binary64))) a (sqrt.f64 b)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* (sqrt b) (sqrt -1))))
#s(approx (sqrt (- a b)) (*.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* 1/2 (* (/ a (sqrt -1)) (sqrt (/ 1 b)))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 a (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (*.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* -1/8 (* (/ a (pow (sqrt -1) 3)) (sqrt (/ 1 (pow b 3))))) (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))))) (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) (fma.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 a (*.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))) a (*.f64 (sqrt.f64 b) (sqrt.f64 #s(literal -1 binary64)))))
#s(approx (sqrt (- a b)) #s(hole binary64 (+ (* a (+ (* 1/2 (* (sqrt (/ 1 b)) (/ 1 (sqrt -1)))) (* a (+ (* -1/8 (* (sqrt (/ 1 (pow b 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (/ a (pow (sqrt -1) 5)) (sqrt (/ 1 (pow b 5))))))))) (* (sqrt b) (sqrt -1)))))
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#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 a a) b)) b) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b)))
#s(approx (sqrt (* (- a b) (+ b a))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (sqrt (- (* a a) (* b b))) (*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) a) a) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 b)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b)) (neg.f64 b)))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))))
#s(approx (* (- a b) (+ b a)) (*.f64 (neg.f64 b) b))
#s(approx (* (- a b) (+ b a)) #s(hole binary64 (* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))))
#s(approx (* (- a b) (+ b a)) (*.f64 (-.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (*.f64 a a) b)) (neg.f64 b)) #s(literal 1 binary64)) (*.f64 b b)))
#s(approx (- a b) #s(hole binary64 (* -1 (* b (+ 1 (* -1 (/ a b)))))))
#s(approx (- a b) (*.f64 (-.f64 #s(literal 1 binary64) (/.f64 a b)) (neg.f64 b)))
#s(approx (+ b a) #s(hole binary64 (* -1 (* b (- (* -1 (/ a b)) 1)))))
#s(approx (+ b a) (*.f64 (-.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64)) (neg.f64 b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (neg.f64 b) (sqrt.f64 #s(literal -1 binary64))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (+.f64 (/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (*.f64 a a) b)) b) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (fma.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1 binary64) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) a) a) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 b)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b)) (neg.f64 b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* (sqrt b) (pow (sqrt -1) 2)))))
#s(approx (sqrt (+ b a)) (*.f64 (sqrt.f64 b) #s(literal 1 binary64)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))
#s(approx (sqrt (+ b a)) (*.f64 (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))) (neg.f64 b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2))))))))
#s(approx (sqrt (+ b a)) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 a a) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) b)))) (neg.f64 b)))
#s(approx (sqrt (+ b a)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (/ (pow a 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (/ (pow a 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* a (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (pow (sqrt -1) 2)))))))))
#s(approx (sqrt (+ b a)) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (/.f64 (*.f64 a a) #s(literal -1 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (fma.f64 (/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (pow.f64 a #s(literal 3 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal 1/16 binary64) (-.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) a) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) b))))) (neg.f64 b)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* (sqrt b) (sqrt -1)))))
#s(approx (sqrt (- a b)) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 b)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))
#s(approx (sqrt (- a b)) (*.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 b)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1))))))))
#s(approx (sqrt (- a b)) (*.f64 (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) a) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 b)))
#s(approx (sqrt (- a b)) #s(hole binary64 (* -1 (* b (+ (* -1/8 (* (* (pow a 2) (sqrt -1)) (sqrt (/ 1 (pow b 5))))) (+ (* 1/16 (* (* (pow a 3) (sqrt -1)) (sqrt (/ 1 (pow b 7))))) (+ (* 1/2 (* (* a (sqrt -1)) (sqrt (/ 1 (pow b 3))))) (* (sqrt (/ 1 b)) (sqrt -1)))))))))
#s(approx (sqrt (- a b)) (*.f64 (fma.f64 (*.f64 (*.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 7 binary64)))) (fma.f64 (*.f64 #s(literal -1/8 binary64) (*.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) a) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 5 binary64)))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) a)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) b)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 b)))

rewrite88.0ms (3.7%)

Memory
-35.8MiB live, 34.7MiB allocated; 53ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02094
03287
111987
096487
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
13 → 190
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
(fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a)
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
(*.f64 a #s(literal -1/2 binary64))
(*.f64 (/.f64 b a) (/.f64 b a))
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(sqrt.f64 (+.f64 b a))
(sqrt.f64 (-.f64 a b))
(/.f64 b a)
Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)
(/.f64 (-.f64 (*.f64 a a) (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 a (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 a a))) (neg.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) a)))
(/.f64 (neg.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (fma.f64 a (-.f64 a (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 a a)) (-.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) a))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (fma.f64 a a (-.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (*.f64 (*.f64 #s(literal -1/2 binary64) a) a)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 3 binary64))) (fma.f64 a (-.f64 a (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64))))
(fma.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64) a)
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) a) (/.f64 (neg.f64 b) a)) (/.f64 (neg.f64 b) a) a)
(fma.f64 (*.f64 (*.f64 #s(literal -1/2 binary64) a) (fabs.f64 (/.f64 b a))) (fabs.f64 (/.f64 b a)) a)
(fma.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1/2 binary64)) a a)
(fma.f64 (*.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) a)) (/.f64 b a) a)
(fma.f64 (/.f64 (neg.f64 b) a) (*.f64 (/.f64 (neg.f64 b) a) (*.f64 #s(literal -1/2 binary64) a)) a)
(fma.f64 (fabs.f64 (/.f64 b a)) (*.f64 (fabs.f64 (/.f64 b a)) (*.f64 #s(literal -1/2 binary64) a)) a)
(fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) a) a)
(fma.f64 (/.f64 b a) (*.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) a)) a)
(fma.f64 (*.f64 #s(literal -1/2 binary64) a) (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a)
(fma.f64 #s(literal -1/2 binary64) (*.f64 a (pow.f64 (/.f64 b a) #s(literal 2 binary64))) a)
(fma.f64 a (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1/2 binary64)) a)
(-.f64 (/.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) a)))
(-.f64 a (*.f64 (neg.f64 (*.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) a))) (/.f64 b a)))
(-.f64 a (*.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (*.f64 #s(literal -1/2 binary64) a)))
(-.f64 a (*.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(-.f64 a (*.f64 (neg.f64 a) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1/2 binary64))))
(+.f64 (/.f64 (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 a (-.f64 a (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a (-.f64 a (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64))) (pow.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) #s(literal 2 binary64)))))
(+.f64 (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)) a)
(+.f64 a (*.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) a) #s(literal -1/2 binary64)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) a) a))
(*.f64 #s(literal -1/2 binary64) a)
(*.f64 a #s(literal -1/2 binary64))
(*.f64 (pow.f64 (/.f64 b a) #s(literal 1 binary64)) (pow.f64 (/.f64 b a) #s(literal 1 binary64)))
(*.f64 (/.f64 (neg.f64 b) (fabs.f64 a)) (/.f64 (neg.f64 b) (fabs.f64 a)))
(*.f64 (/.f64 (fabs.f64 b) (neg.f64 a)) (/.f64 (fabs.f64 b) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 b) a) (/.f64 (fabs.f64 b) a))
(*.f64 (/.f64 b (fabs.f64 a)) (/.f64 b (fabs.f64 a)))
(*.f64 (neg.f64 (fabs.f64 (/.f64 b a))) (neg.f64 (fabs.f64 (/.f64 b a))))
(*.f64 (fabs.f64 (fabs.f64 (/.f64 b a))) (fabs.f64 (fabs.f64 (/.f64 b a))))
(*.f64 (/.f64 (neg.f64 b) a) (/.f64 (neg.f64 b) a))
(*.f64 (neg.f64 b) (/.f64 (neg.f64 b) (*.f64 a a)))
(*.f64 (fabs.f64 (/.f64 b a)) (fabs.f64 (/.f64 b a)))
(*.f64 (fabs.f64 b) (/.f64 (fabs.f64 b) (*.f64 a a)))
(*.f64 (/.f64 b a) (/.f64 b a))
(*.f64 b (/.f64 (/.f64 b a) a))
(*.f64 b (/.f64 b (*.f64 a a)))
(pow.f64 (/.f64 (neg.f64 b) a) #s(literal 2 binary64))
(pow.f64 (fabs.f64 (/.f64 b a)) #s(literal 2 binary64))
(pow.f64 (/.f64 b a) #s(literal 2 binary64))
(/.f64 (/.f64 (*.f64 b b) (neg.f64 a)) (neg.f64 a))
(/.f64 (/.f64 (*.f64 b b) (fabs.f64 a)) (fabs.f64 a))
(/.f64 (*.f64 (neg.f64 b) (/.f64 b a)) (neg.f64 a))
(/.f64 (*.f64 (/.f64 b a) (neg.f64 b)) (neg.f64 a))
(/.f64 (neg.f64 (*.f64 (/.f64 b a) b)) (neg.f64 a))
(/.f64 (*.f64 (/.f64 b a) b) a)
(/.f64 (*.f64 (neg.f64 b) b) (*.f64 (neg.f64 a) a))
(/.f64 (*.f64 (neg.f64 b) b) (*.f64 a (neg.f64 a)))
(/.f64 (*.f64 (neg.f64 b) b) (neg.f64 (*.f64 a a)))
(/.f64 (*.f64 b b) (*.f64 a a))
(neg.f64 (*.f64 (/.f64 (neg.f64 b) a) (/.f64 b a)))
(neg.f64 (*.f64 (/.f64 b a) (/.f64 (neg.f64 b) a)))
(fabs.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (/.f64 b a)) #s(literal 2 binary64)))
(*.f64 (pow.f64 (*.f64 (+.f64 b a) (-.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 b a) (-.f64 a b)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(pow.f64 (*.f64 (+.f64 b a) (-.f64 a b)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (hypot.f64 b a))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 b a) (-.f64 a b))) #s(literal 1/2 binary64)))
(*.f64 (+.f64 (neg.f64 a) (neg.f64 b)) (-.f64 (neg.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (neg.f64 a) (fabs.f64 b)) (-.f64 (neg.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (neg.f64 a) b) (-.f64 (neg.f64 a) b))
(*.f64 (+.f64 (fabs.f64 a) (neg.f64 b)) (-.f64 (fabs.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) (fabs.f64 b)) (-.f64 (fabs.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) b) (-.f64 (fabs.f64 a) b))
(*.f64 (+.f64 a (neg.f64 b)) (-.f64 a (neg.f64 b)))
(*.f64 (+.f64 a (fabs.f64 b)) (-.f64 a (fabs.f64 b)))
(*.f64 (+.f64 b a) (-.f64 a b))
(*.f64 (-.f64 a b) (+.f64 b a))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (-.f64 a b)) (-.f64 b a))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b)) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 b a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 b a)) (+.f64 b a))
(/.f64 (*.f64 (+.f64 b a) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b (+.f64 b a) (*.f64 a a)))
(/.f64 (*.f64 (+.f64 b a) (*.f64 (+.f64 b a) (-.f64 a b))) (+.f64 b a))
(/.f64 (*.f64 (-.f64 a b) (*.f64 (+.f64 b a) (-.f64 b a))) (-.f64 b a))
(/.f64 (*.f64 (-.f64 a b) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b)) (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a))) (-.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a)))
(/.f64 (+.f64 (pow.f64 (*.f64 (-.f64 a b) b) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 a b) a) #s(literal 3 binary64))) (fma.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b) (-.f64 (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a)) (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a)))))
(/.f64 (+.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 b) b) #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (*.f64 a a) (*.f64 (neg.f64 b) b)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (neg.f64 (fma.f64 b b (*.f64 a a))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (neg.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (-.f64 b a) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 (+.f64 b a) (-.f64 a b))) (*.f64 (-.f64 b a) (+.f64 b a)))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (fma.f64 (-.f64 a b) a (*.f64 b b)) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (+.f64 b a) (-.f64 a b))) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (+.f64 b a) (-.f64 b a))) (*.f64 (fma.f64 b (+.f64 b a) (*.f64 a a)) (-.f64 b a)))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (fma.f64 b (+.f64 b a) (*.f64 a a)) (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (*.f64 (+.f64 b a) (-.f64 b a))) (*.f64 (+.f64 b a) (-.f64 b a)))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (+.f64 b a) (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (-.f64 a b) b (*.f64 (-.f64 a b) a))
(fma.f64 (-.f64 a b) a (*.f64 (-.f64 a b) b))
(fma.f64 b (neg.f64 b) (*.f64 a a))
(fma.f64 b (-.f64 a b) (*.f64 (-.f64 a b) a))
(fma.f64 a (-.f64 a b) (*.f64 (-.f64 a b) b))
(fma.f64 a a (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 a a (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (*.f64 (-.f64 a b) b) (*.f64 (neg.f64 a) (-.f64 a b)))
(-.f64 (*.f64 (-.f64 a b) b) (*.f64 (neg.f64 (-.f64 a b)) a))
(-.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) b))
(-.f64 (*.f64 a a) (*.f64 b b))
(+.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) b))
(+.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (*.f64 (+.f64 b a) (-.f64 b a))) (-.f64 b a))
(*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(*.f64 (+.f64 b a) (/.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (/.f64 (+.f64 b a) (+.f64 b a)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (neg.f64 (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (neg.f64 (*.f64 (+.f64 b a) (-.f64 a b))) (neg.f64 (+.f64 b a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (*.f64 (fma.f64 b b (*.f64 a a)) (+.f64 b a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b (+.f64 b a) (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (*.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))) (+.f64 b a)))
(/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 b a))
(-.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(-.f64 (/.f64 (*.f64 a a) (+.f64 b a)) (/.f64 (*.f64 b b) (+.f64 b a)))
(-.f64 a b)
(+.f64 (/.f64 (*.f64 (-.f64 a b) b) (+.f64 b a)) (/.f64 (*.f64 (-.f64 a b) a) (+.f64 b a)))
(+.f64 (/.f64 (*.f64 a a) (+.f64 b a)) (/.f64 (*.f64 (neg.f64 b) b) (+.f64 b a)))
(/.f64 (neg.f64 (*.f64 (+.f64 b a) (-.f64 b a))) (neg.f64 (-.f64 b a)))
(/.f64 (neg.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (-.f64 b a))
(/.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 a a (-.f64 (*.f64 b b) (*.f64 b a))))
(/.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (-.f64 a b))
(-.f64 (/.f64 (*.f64 b b) (-.f64 b a)) (/.f64 (*.f64 a a) (-.f64 b a)))
(+.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 a b) a (*.f64 b b))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 a b) a (*.f64 b b))))
(+.f64 b a)
(+.f64 a b)
(*.f64 (pow.f64 (*.f64 (+.f64 b a) (-.f64 a b)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (+.f64 b a) (-.f64 a b)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (-.f64 a b)) (sqrt.f64 (+.f64 b a)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
(pow.f64 (*.f64 (+.f64 b a) (-.f64 a b)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (hypot.f64 b a))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (sqrt.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b)))
(exp.f64 (*.f64 (log.f64 (*.f64 (+.f64 b a) (-.f64 a b))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 b a) #s(literal 1/4 binary64)) (pow.f64 (+.f64 b a) #s(literal 1/4 binary64)))
(pow.f64 (+.f64 b a) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (*.f64 (+.f64 b a) (-.f64 b a))) (sqrt.f64 (-.f64 b a)))
(/.f64 (hypot.f64 (pow.f64 a #s(literal 3/2 binary64)) (pow.f64 b #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 a b) a (*.f64 b b))))
(sqrt.f64 (+.f64 b a))
(exp.f64 (*.f64 (log.f64 (+.f64 b a)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)) (pow.f64 (-.f64 a b) #s(literal 1/4 binary64)))
(pow.f64 (-.f64 a b) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (sqrt.f64 (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 b a) (-.f64 a b))) (sqrt.f64 (+.f64 b a)))
(sqrt.f64 (-.f64 a b))
(exp.f64 (*.f64 (log.f64 (-.f64 a b)) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 a)))
(/.f64 (neg.f64 b) (neg.f64 a))
(/.f64 b a)
(neg.f64 (/.f64 (neg.f64 b) a))

eval40.0ms (1.7%)

Memory
-6.4MiB live, 41.0MiB allocated; 8ms collecting garbage
Compiler

Compiled 7 962 to 1 263 computations (84.1% saved)

prune7.0ms (0.3%)

Memory
15.5MiB live, 15.5MiB allocated; 0ms collecting garbage
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New3521353
Fresh000
Picked134
Done000
Total3534357
Accuracy
100.0%
Counts
357 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.3%
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
✓54.3%
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
▶99.2%
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
✓98.6%
#s(approx (sqrt (- (* a a) (* b b))) a)
Compiler

Compiled 45 to 32 computations (28.9% saved)

simplify11.0ms (0.5%)

Memory
6.2MiB live, 6.2MiB allocated; 0ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 b a)
cost-diff0
(*.f64 b #s(literal -1/2 binary64))
cost-diff0
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
cost-diff0
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01235
01635
12535
24535
39535
418935
530235
645535
747635
047635
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
(*.f64 b #s(literal -1/2 binary64))
b
#s(literal -1/2 binary64)
(/.f64 b a)
a
Outputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
(fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a)
(*.f64 b #s(literal -1/2 binary64))
(*.f64 #s(literal -1/2 binary64) b)
b
#s(literal -1/2 binary64)
(/.f64 b a)
a

localize30.0ms (1.2%)

Memory
-24.7MiB live, 22.2MiB allocated; 2ms collecting garbage
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
accuracy0.0
(/.f64 b a)
accuracy0.0
(*.f64 b #s(literal -1/2 binary64))
accuracy0.518177132210616
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
Samples
22.0ms256×0valid
Compiler

Compiled 29 to 14 computations (51.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 4.0ms (26.9% of total)
ival-div: 3.0ms (20.2% of total)
ival-add: 3.0ms (20.2% of total)
ival-sqrt: 3.0ms (20.2% of total)
ival-sub: 1.0ms (6.7% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.2%)

Memory
5.8MiB live, 5.8MiB allocated; 0ms collecting garbage
Counts
4 → 31
Calls
Call 1
Inputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
(*.f64 b #s(literal -1/2 binary64))
(/.f64 b a)
Outputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (/ b a) #s(hole binary64 (/ b a)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 a))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (* b -1/2) #s(hole binary64 (* -1/2 b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
b
@-inf
((* (sqrt (+ b a)) (sqrt (- a b))) (+ (* (* b -1/2) (/ b a)) a) (* b -1/2) (/ b a))
1.0ms
b
@inf
((* (sqrt (+ b a)) (sqrt (- a b))) (+ (* (* b -1/2) (/ b a)) a) (* b -1/2) (/ b a))
1.0ms
a
@-inf
((* (sqrt (+ b a)) (sqrt (- a b))) (+ (* (* b -1/2) (/ b a)) a) (* b -1/2) (/ b a))
1.0ms
a
@0
((* (sqrt (+ b a)) (sqrt (- a b))) (+ (* (* b -1/2) (/ b a)) a) (* b -1/2) (/ b a))
1.0ms
a
@inf
((* (sqrt (+ b a)) (sqrt (- a b))) (+ (* (* b -1/2) (/ b a)) a) (* b -1/2) (/ b a))

simplify135.0ms (5.6%)

Memory
30.6MiB live, 76.0MiB allocated; 6ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0235954
1802676
24767647
08435619
Stop Event
1×iter limit
1×node limit
Counts
31 → 31
Calls
Call 1
Inputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (/ b a) #s(hole binary64 (/ b a)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 a))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (* b -1/2) #s(hole binary64 (* -1/2 b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
Outputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (sqrt -1))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* 1/2 (/ (* a (+ b (* -1 b))) (* b (sqrt -1)))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (* a (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2)))))) (* b (sqrt -1)))) (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) a) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) b) b)) #s(literal 0 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ (* a (+ (* 1/2 (/ (+ b (* -1 b)) (* b (sqrt -1)))) (* a (+ (* -1/4 (/ (* a (* (+ b (* -1 b)) (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))))) (* (pow b 3) (pow (sqrt -1) 3)))) (* 1/2 (/ (- 1 (* 1/4 (/ (pow (+ b (* -1 b)) 2) (* (pow b 2) (pow (sqrt -1) 2))))) (* b (sqrt -1)))))))) (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (+.f64 (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 (/.f64 #s(literal 0 binary64) b) b)) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64))) (/.f64 (fma.f64 (*.f64 #s(literal 1/2 binary64) a) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 0 binary64) b) b)) #s(literal 0 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))) a (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* -1/2 (/ (pow b 2) a))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) (*.f64 (*.f64 b (/.f64 b a)) #s(literal -1/2 binary64)))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (/ (+ (* -1/2 (pow b 2)) (pow a 2)) a)))
#s(approx (+ (* (* b -1/2) (/ b a)) a) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
#s(approx (/ b a) #s(hole binary64 (/ b a)))
#s(approx (/ b a) (/.f64 b a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) a)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (* 1/2 (/ (+ b (* -1 b)) a))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) a)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) a) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* a (+ 1 (+ (* -1/4 (/ (* (+ b (* -1 b)) (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2)))) (pow a 3))) (+ (* 1/2 (/ (+ b (* -1 b)) a)) (* 1/2 (/ (- (* -1 (pow b 2)) (* 1/4 (pow (+ b (* -1 b)) 2))) (pow a 2)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) a) a))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 a))
#s(approx (+ (* (* b -1/2) (/ b a)) a) a)
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* a (+ 1 (* -1/2 (/ (pow b 2) (pow a 2)))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) (*.f64 (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) a) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (pow (sqrt -1) 2)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) a)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1/2 (/ (+ b (* -1 b)) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) a)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1/2 (/ (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) a) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* a (+ (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ b (* -1 b)) (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2))))) (* a (pow (sqrt -1) 2)))) (* 1/2 (- (pow b 2) (* 1/4 (/ (pow (+ b (* -1 b)) 2) (pow (sqrt -1) 2)))))) a)) (* 1/2 (+ b (* -1 b)))) a)) (pow (sqrt -1) 2))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) a) a))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* -1 (* a (- (* 1/2 (/ (pow b 2) (pow a 2))) 1)))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) (*.f64 (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) a) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* 1/2 (/ (* b (+ a (* -1 a))) a)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) a)
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* -1/2 (/ (* b (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2))))) a)) (* 1/2 (/ (+ a (* -1 a)) a)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (+ a (* b (+ (* 1/2 (/ (+ a (* -1 a)) a)) (* b (+ (* -1/2 (/ (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) a)) (* 1/4 (/ (* b (* (+ 1 (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow a 2)))) (+ a (* -1 a)))) (pow a 3))))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (+ a (* -1/2 (/ (pow b 2) a)))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
#s(approx (* b -1/2) #s(hole binary64 (* -1/2 b)))
#s(approx (* b -1/2) (*.f64 #s(literal -1/2 binary64) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (/.f64 (*.f64 a a) b) #s(literal -1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal -1 binary64))) b)) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* b (+ (sqrt -1) (+ (* -1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* (pow b 3) (pow (sqrt -1) 3)))) (+ (* 1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* (pow b 2) (sqrt -1))))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (fma.f64 (/.f64 (/.f64 (+.f64 #s(literal 0 binary64) (/.f64 (*.f64 a a) b)) b) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64) (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 0 binary64) (pow.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) b) #s(literal 3 binary64))))) b))
#s(approx (+ (* (* b -1/2) (/ b a)) a) #s(hole binary64 (* (pow b 2) (- (/ a (pow b 2)) (* 1/2 (/ 1 a))))))
#s(approx (+ (* (* b -1/2) (/ b a)) a) (*.f64 (-.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal 1/2 binary64) a)) (*.f64 b b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (sqrt -1)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) b))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1/2 (/ (+ a (* -1 a)) (* b (sqrt -1)))))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) b (/.f64 #s(literal 0 binary64) (*.f64 (sqrt.f64 #s(literal -1 binary64)) b)))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (* b (sqrt -1)))) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (/.f64 (fma.f64 (/.f64 (*.f64 a a) b) #s(literal -1/2 binary64) #s(literal 0 binary64)) (sqrt.f64 #s(literal -1 binary64))) b)) (neg.f64 b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) #s(hole binary64 (* -1 (* b (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ a (* -1 a)) (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2))))) (* b (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow a 2) (* 1/4 (/ (pow (+ a (* -1 a)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) b)) (* 1/2 (/ (+ a (* -1 a)) (sqrt -1)))) b)))))))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (*.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 (/.f64 (fma.f64 (*.f64 a a) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) b)) (sqrt.f64 #s(literal -1 binary64))) (neg.f64 b)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) b)) (neg.f64 b)))

rewrite164.0ms (6.8%)

Memory
-16.9MiB live, 121.1MiB allocated; 15ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01232
01631
16431
243731
3599231
0804231
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 78
Calls
Call 1
Inputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
(fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a)
(*.f64 b #s(literal -1/2 binary64))
(/.f64 b a)
Outputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a)) (-.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 a #s(literal 3 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 a (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a))) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64))) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))))))
(*.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64))) (+.f64 (pow.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) (-.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64))))
(*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)) (/.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(*.f64 (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) (/.f64 (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a))) (*.f64 (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))) (+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a))))
(/.f64 (-.f64 (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))) (*.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))) (-.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))
(/.f64 (-.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) #s(literal 3 binary64)) (pow.f64 (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (fma.f64 (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a))))))
(/.f64 (+.f64 (pow.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) #s(literal 3 binary64))) (fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (-.f64 (*.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))) (*.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 a a) (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)))) (neg.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a)))) (neg.f64 (neg.f64 (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))))
(/.f64 (-.f64 (*.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (*.f64 (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a) (*.f64 a a))) (*.f64 (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(/.f64 (fma.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)) (*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)) (pow.f64 a #s(literal 3 binary64)))) (*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (*.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 a a)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (*.f64 (fma.f64 (*.f64 a a) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 a a)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64))) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(/.f64 (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (*.f64 (-.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 a #s(literal 3 binary64))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(/.f64 (-.f64 (*.f64 a a) (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))))
(/.f64 (+.f64 (pow.f64 a #s(literal 9 binary64)) (pow.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) #s(literal 9 binary64))) (*.f64 (-.f64 (+.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))) (pow.f64 (*.f64 (*.f64 a (*.f64 (/.f64 b a) b)) #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a))) (neg.f64 (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64)))) (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a))
(/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a))) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a)) (neg.f64 (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a))))
(neg.f64 (/.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64) (pow.f64 a #s(literal 3 binary64))) (neg.f64 (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a)))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (+.f64 (pow.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) (-.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (pow.f64 a #s(literal 3 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 a (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a))) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) a))) (fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (-.f64 (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64)) (pow.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) #s(literal 2 binary64)))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (neg.f64 a) (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (+.f64 (pow.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 6 binary64)))) (fma.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) (-.f64 (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a) (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64))) (pow.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) #s(literal 4 binary64))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 b b)) (/.f64 b a)) (/.f64 (/.f64 b a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) b)) (/.f64 (*.f64 #s(literal -1/2 binary64) b) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 (*.f64 (/.f64 b a) b) (*.f64 #s(literal -1/2 binary64) b)) (/.f64 (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64) a)
(fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 b b)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 b b)) (/.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (pow.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) #s(literal 3/2 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (pow.f64 a #s(literal 3/2 binary64)) (/.f64 (pow.f64 a #s(literal 3/2 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) (/.f64 (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 (fabs.f64 (*.f64 (/.f64 b a) b)) #s(literal 1/2 binary64)) (/.f64 (*.f64 (fabs.f64 (*.f64 (/.f64 b a) b)) #s(literal 1/2 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) (/.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 3 binary64))) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (*.f64 #s(literal -1/8 binary64) (pow.f64 b #s(literal 3 binary64))) (/.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) b a)
(fma.f64 (*.f64 b b) (/.f64 (pow.f64 (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) #s(literal 2 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (pow.f64 b #s(literal 3 binary64)) (/.f64 (pow.f64 (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (*.f64 a a) (/.f64 a (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (/.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (neg.f64 b) (/.f64 (*.f64 #s(literal -1/2 binary64) b) (neg.f64 a)) a)
(fma.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) (/.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 (/.f64 b a) (/.f64 (*.f64 (*.f64 #s(literal 1/4 binary64) (*.f64 b b)) (/.f64 b a)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (/.f64 b a) (*.f64 #s(literal -1/2 binary64) b) a)
(fma.f64 (*.f64 #s(literal -1/2 binary64) b) (/.f64 (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (*.f64 #s(literal -1/2 binary64) b)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 (*.f64 #s(literal -1/2 binary64) b) (/.f64 b a) a)
(fma.f64 #s(literal -1/2 binary64) (*.f64 (/.f64 b a) b) a)
(fma.f64 a (/.f64 (*.f64 a a) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(fma.f64 b (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) #s(literal 2 binary64)) b) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(fma.f64 b (*.f64 (/.f64 b a) #s(literal -1/2 binary64)) a)
(-.f64 (/.f64 (*.f64 a a) (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)))))
(-.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 a a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(-.f64 a (*.f64 (*.f64 #s(literal 1/2 binary64) b) (/.f64 b a)))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 3 binary64)) #s(literal -1/8 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64) (*.f64 (-.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64))) a))))
(+.f64 (/.f64 (*.f64 (pow.f64 (*.f64 (/.f64 b a) b) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)) (/.f64 (*.f64 (neg.f64 a) a) (-.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)))
(+.f64 (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)) a)
(+.f64 a (*.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) b)) (/.f64 b a)))
(+.f64 a (*.f64 (*.f64 (/.f64 b a) b) #s(literal -1/2 binary64)))
(*.f64 #s(literal -1/2 binary64) b)
(*.f64 b #s(literal -1/2 binary64))
(/.f64 (neg.f64 b) (neg.f64 a))
(/.f64 b a)
(neg.f64 (/.f64 (neg.f64 b) a))

eval10.0ms (0.4%)

Memory
19.6MiB live, 19.6MiB allocated; 0ms collecting garbage
Compiler

Compiled 4 723 to 411 computations (91.3% saved)

prune6.0ms (0.2%)

Memory
-38.6MiB live, 8.4MiB allocated; 2ms collecting garbage
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New97097
Fresh000
Picked011
Done033
Total974101
Accuracy
100.0%
Counts
101 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓99.3%
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
✓54.3%
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
✓99.2%
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
✓98.6%
#s(approx (sqrt (- (* a a) (* b b))) a)
Compiler

Compiled 119 to 64 computations (46.2% saved)

regimes13.0ms (0.5%)

Memory
14.4MiB live, 14.4MiB allocated; 0ms collecting garbage
Counts
6 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
#s(approx (sqrt (- (* a a) (* b b))) (fma.f64 (*.f64 a #s(literal -1/2 binary64)) (*.f64 (/.f64 b a) (/.f64 b a)) a))
Outputs
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
Calls

6 calls:

2.0ms
b
2.0ms
a
2.0ms
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
2.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
2.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
99.3%1(*.f64 b b)
99.3%1(*.f64 a a)
99.3%1(-.f64 (*.f64 a a) (*.f64 b b))
99.3%1(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
99.3%1a
99.3%1b
Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes10.0ms (0.4%)

Memory
12.2MiB live, 12.2MiB allocated; 0ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
Outputs
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
Calls

6 calls:

2.0ms
b
2.0ms
a
2.0ms
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
2.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
2.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
99.2%1(*.f64 b b)
99.2%1(*.f64 a a)
99.2%1(-.f64 (*.f64 a a) (*.f64 b b))
99.2%1(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
99.2%1a
99.2%1b
Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes7.0ms (0.3%)

Memory
10.6MiB live, 10.6MiB allocated; 0ms collecting garbage
Accuracy

Total -29.0b remaining (-3215.9%)

Threshold costs -29b (-3215.9%)

Counts
2 → 1
Calls
Call 1
Inputs
#s(approx (sqrt (- (* a a) (* b b))) a)
(sqrt.f64 (*.f64 (-.f64 a b) (+.f64 b a)))
Outputs
#s(approx (sqrt (- (* a a) (* b b))) a)
Calls

6 calls:

1.0ms
a
1.0ms
b
1.0ms
(*.f64 a a)
1.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
1.0ms
(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
Results
AccuracySegmentsBranch
98.6%1(*.f64 b b)
98.6%1(*.f64 a a)
98.6%1(-.f64 (*.f64 a a) (*.f64 b b))
98.6%1(sqrt.f64 (-.f64 (*.f64 a a) (*.f64 b b)))
98.6%1a
98.6%1b
Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify59.0ms (2.5%)

Memory
-38.2MiB live, 16.8MiB allocated; 4ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02237
13837
210237
324537
442337
585237
6140537
7208937
8291437
9322437
10328637
11328637
12336437
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
#s(approx (sqrt (- (* a a) (* b b))) a)
Outputs
(*.f64 (sqrt.f64 (+.f64 b a)) (sqrt.f64 (-.f64 a b)))
#s(approx (* (sqrt (+ b a)) (sqrt (- a b))) (fma.f64 (*.f64 b #s(literal -1/2 binary64)) (/.f64 b a) a))
#s(approx (sqrt (- (* a a) (* b b))) a)

derivations222.0ms (9.2%)

Memory
16.7MiB live, 62.6MiB allocated; 3ms collecting garbage
Stop Event
1×done
Compiler

Compiled 37 to 22 computations (40.5% saved)

preprocess26.0ms (1.1%)

Memory
-17.5MiB live, 28.2MiB allocated; 4ms collecting garbage
Remove

(abs b)

Compiler

Compiled 170 to 116 computations (31.8% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Profiling

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