Eccentricity of an ellipse

Time bar (total: 4.9s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze50.0ms (1%)

Memory
-21.2MiB live, 27.9MiB allocated
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%37.5%62.5%0%0%0%0
0%0%37.5%62.5%0%0%0%1
0%0%18.7%62.5%0%18.7%0%2
0%0%9.4%62.5%0%28.1%0%3
0%0%9.4%62.5%0%28.1%0%4
0%0%7%62.5%0%30.4%0%5
20%1.2%4.7%62.5%0%31.6%0%6
25%1.2%3.5%62.5%0%32.8%0%7
40%1.8%2.6%62.5%0%33.1%0%8
51.9%2%1.9%62.5%0%33.5%0%9
64.7%2.4%1.3%62.5%0%33.7%0%10
72.9%2.6%1%62.5%0%33.9%0%11
80.2%2.7%0.7%62.5%0%34%0%12
Compiler

Compiled 25 to 16 computations (36% saved)

sample2.2s (44.9%)

Memory
-17.1MiB live, 1 585.9MiB allocated
Samples
770.0ms8 256×0valid
143.0ms794×0invalid
Precisions
Click to see histograms. Total time spent on operations: 638.0ms
ival-<=: 186.0ms (29.1% of total)
ival-mult: 158.0ms (24.8% of total)
ival-sqrt: 78.0ms (12.2% of total)
ival-div: 73.0ms (11.4% of total)
ival-fabs: 67.0ms (10.5% of total)
ival-sub: 43.0ms (6.7% of total)
ival-and: 19.0ms (3% of total)
exact: 11.0ms (1.7% of total)
ival-assert: 4.0ms (0.6% of total)
Bogosity

explain120.0ms (2.4%)

Memory
11.2MiB live, 156.3MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
510-0-(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
00-0-(*.f64 a a)
00-0-a
00-0-b
00-0-(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
00-0-(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
00-0-(-.f64 (*.f64 a a) (*.f64 b b))
00-0-(*.f64 b b)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
/.f64(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))u/u510
↳(*.f64 b b)underflow176
↳(-.f64 (*.f64 a a) (*.f64 b b))underflow51
↳(*.f64 a a)underflow51
↳(*.f64 a a)underflow51
Confusion
Predicted +Predicted -
+510
-0205
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+5100
-00205
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0205
151
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
54.0ms512×0valid
Compiler

Compiled 119 to 28 computations (76.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 41.0ms
ival-sqrt: 26.0ms (63.2% of total)
ival-mult: 6.0ms (14.6% of total)
ival-div: 3.0ms (7.3% of total)
ival-sub: 2.0ms (4.9% of total)
ival-fabs: 2.0ms (4.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess115.0ms (2.3%)

Memory
4.1MiB live, 144.1MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02267
18857
258657
3309957
0813
01413
13711
220411
3143411
0873910
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
Symmetry

(abs b)

(abs a)

Compiler

Compiled 13 to 8 computations (38.5% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.6MiB live, 0.6MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶80.1%
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
Compiler

Compiled 13 to 8 computations (38.5% saved)

simplify124.0ms (2.5%)

Memory
-2.8MiB live, 99.0MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(-.f64 (*.f64 a a) (*.f64 b b))
cost-diff0
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
cost-diff1
(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
cost-diff2
(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0851
01451
13745
220445
3143445
0873943
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b
Outputs
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
(fma.f64 (/.f64 (/.f64 (neg.f64 b) a) a) b #s(literal 1 binary64))
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 a a)
a
(*.f64 b b)
b

localize32.0ms (0.7%)

Memory
-21.2MiB live, 25.3MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
accuracy0.00390625
(-.f64 (*.f64 a a) (*.f64 b b))
accuracy0.00390625
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
accuracy12.363421554025535
(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
Samples
26.0ms256×0valid
Compiler

Compiled 53 to 10 computations (81.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 20.0ms
ival-mult: 14.0ms (69.8% of total)
ival-div: 2.0ms (10% of total)
ival-sqrt: 2.0ms (10% of total)
ival-sub: 1.0ms (5% of total)
ival-fabs: 1.0ms (5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
4.3MiB live, 4.3MiB allocated
Counts
4 → 13
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (pow a 2)) (pow a 2))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
1
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Calls

6 calls:

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

simplify129.0ms (2.6%)

Memory
28.1MiB live, 124.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
025117
158104
2194104
31182104
45531104
08296101
Stop Event
1×iter limit
1×node limit
Counts
13 → 13
Calls
Call 1
Inputs
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (pow a 2)) (pow a 2))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
1
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Outputs
(* -1 (/ (pow b 2) (pow a 2)))
(*.f64 (/.f64 (/.f64 (neg.f64 b) a) a) b)
(/ (+ (* -1 (pow b 2)) (pow a 2)) (pow a 2))
(/.f64 (fma.f64 (/.f64 b a) (neg.f64 b) a) a)
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(*.f64 (-.f64 a b) (+.f64 b a))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(/.f64 (fma.f64 (/.f64 b a) (neg.f64 b) a) a)
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (-.f64 a b) (+.f64 b a))
(+ (* -1 (pow b 2)) (pow a 2))
(*.f64 (-.f64 a b) (+.f64 b a))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 b b)) (/.f64 (/.f64 #s(literal 1 binary64) a) a)) (*.f64 b b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (*.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) b) b)

rewrite78.0ms (1.6%)

Memory
3.9MiB live, 96.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0843
01442
16036
256026
0912725
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
4 → 403
Calls
Call 1
Inputs
(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(*.f64 (/.f64 (fma.f64 b b (*.f64 a a)) (fma.f64 b b (*.f64 a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) (neg.f64 a)) (/.f64 (fabs.f64 (-.f64 b a)) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) a) (/.f64 (fabs.f64 (-.f64 b a)) a))
(*.f64 (/.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) (neg.f64 a)) (/.f64 (-.f64 (neg.f64 a) b) a))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) (neg.f64 a)) (/.f64 (-.f64 (neg.f64 a) b) (neg.f64 a)))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) a) (/.f64 (-.f64 (neg.f64 a) b) a))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) a) (/.f64 (-.f64 (neg.f64 a) b) (neg.f64 a)))
(*.f64 (neg.f64 (/.f64 (hypot.f64 b a) a)) (neg.f64 (/.f64 (hypot.f64 b a) a)))
(*.f64 (fabs.f64 (/.f64 (+.f64 b a) a)) (fabs.f64 (/.f64 (-.f64 a b) a)))
(*.f64 (/.f64 (/.f64 (-.f64 a b) a) a) (+.f64 b a))
(*.f64 (+.f64 (neg.f64 b) a) (/.f64 (-.f64 (neg.f64 a) b) (*.f64 a a)))
(*.f64 (+.f64 (neg.f64 b) a) (/.f64 (-.f64 (neg.f64 a) b) (*.f64 (neg.f64 a) a)))
(*.f64 (/.f64 (-.f64 a b) a) (/.f64 (+.f64 b a) a))
(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
(*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (/.f64 (fma.f64 b b (*.f64 a a)) (*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (*.f64 a a))))
(*.f64 (fabs.f64 (+.f64 b a)) (/.f64 (fabs.f64 (-.f64 b a)) (*.f64 a a)))
(*.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 (/.f64 (/.f64 (-.f64 a b) a) a)))
(*.f64 (/.f64 (hypot.f64 b a) a) (/.f64 (hypot.f64 b a) a))
(*.f64 (-.f64 a b) (/.f64 (+.f64 b a) (*.f64 a a)))
(*.f64 (-.f64 a b) (/.f64 (+.f64 b a) (*.f64 (neg.f64 a) a)))
(*.f64 (+.f64 b a) (/.f64 (/.f64 (-.f64 a b) a) a))
(*.f64 (fma.f64 b b (*.f64 a a)) (/.f64 (fma.f64 b b (*.f64 a a)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
(pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))
(pow.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (/.f64 (*.f64 (hypot.f64 b a) (hypot.f64 b a)) (neg.f64 a)) (neg.f64 a))
(/.f64 (/.f64 (*.f64 (hypot.f64 b a) (hypot.f64 b a)) (neg.f64 a)) a)
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 3 binary64))) (neg.f64 a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 3 binary64))) a)
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (*.f64 (neg.f64 a) a)) (*.f64 (neg.f64 a) a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (neg.f64 a)) (pow.f64 a #s(literal 3 binary64)))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (*.f64 a a)) (*.f64 a a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) a) (pow.f64 a #s(literal 3 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (/.f64 (/.f64 (-.f64 a b) a) a)) (fma.f64 b (-.f64 b a) (*.f64 a a)))
(/.f64 (*.f64 (fma.f64 b b (*.f64 a a)) (/.f64 (/.f64 (-.f64 a b) a) a)) (-.f64 a b))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) (neg.f64 a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (*.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))))
(/.f64 (neg.f64 (fabs.f64 (/.f64 (fma.f64 b b (*.f64 a a)) a))) (neg.f64 a))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))))) (neg.f64 (fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (/.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 6 binary64))))) (fma.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) #s(literal 1 binary64)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))) (pow.f64 a #s(literal 4 binary64)))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b)) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (*.f64 a a)))
(/.f64 (*.f64 (fma.f64 b b (*.f64 a a)) (-.f64 a b)) (*.f64 (-.f64 a b) (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (*.f64 (+.f64 (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (*.f64 b a) #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (*.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (*.f64 a a))))
(/.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (*.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
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(+.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a 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 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 (neg.f64 a) a))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 a a))
(+.f64 (*.f64 (neg.f64 a) a) (*.f64 (neg.f64 b) b))
(+.f64 (*.f64 (neg.f64 a) a) (*.f64 b b))
(+.f64 (*.f64 b b) (*.f64 (neg.f64 a) a))
(+.f64 (*.f64 b b) (*.f64 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(+.f64 (*.f64 a a) (*.f64 b b))

eval44.0ms (0.9%)

Memory
-36.1MiB live, 63.2MiB allocated
Compiler

Compiled 6 154 to 1 251 computations (79.7% saved)

prune5.0ms (0.1%)

Memory
14.2MiB live, 14.2MiB allocated
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2854289
Fresh000
Picked101
Done000
Total2864290
Accuracy
100.0%
Counts
290 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
▶80.1%
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
▶98.1%
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
▶100.0%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
Compiler

Compiled 64 to 42 computations (34.4% saved)

simplify78.0ms (1.6%)

Memory
-11.3MiB live, 81.9MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
cost-diff0
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
cost-diff1
(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
cost-diff2
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
cost-diff0
(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff0
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
cost-diff1
(fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a)))
cost-diff2
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))
cost-diff0
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
cost-diff0
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
cost-diff0
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
cost-diff0
(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
cost-diff0
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
cost-diff0
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
cost-diff0
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
030228
050222
1111204
2373200
32321198
08907198
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
(/.f64 (/.f64 b a) a)
(/.f64 b a)
b
a
#s(literal -1 binary64)
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
(fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a)))
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 a a)
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(/.f64 (+.f64 b a) a)
(+.f64 b a)
b
a
(-.f64 a b)
Outputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
(/.f64 (/.f64 b a) a)
(/.f64 b a)
b
a
#s(literal -1 binary64)
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a)))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))
(neg.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(-.f64 a b)
a
b
(+.f64 b a)
(*.f64 a a)
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(neg.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(/.f64 (+.f64 b a) a)
(+.f64 b a)
b
a
(-.f64 a b)

localize67.0ms (1.4%)

Memory
35.9MiB live, 82.2MiB allocated
Localize:

Found 15 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
accuracy0.01953125
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
accuracy0.03125
(/.f64 (+.f64 b a) a)
accuracy0.0546875
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
accuracy0.0
(*.f64 a a)
accuracy0.0
(fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a)))
accuracy0.00390625
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
accuracy12.363421554025535
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))
accuracy0.0
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
accuracy0.00390625
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
accuracy1.2582199636917244
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
accuracy0.0
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
accuracy0.0
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
accuracy0.00390625
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
accuracy0.2890625
(/.f64 (/.f64 b a) a)
Samples
52.0ms256×0valid
Compiler

Compiled 206 to 28 computations (86.4% saved)

Precisions
Click to see histograms. Total time spent on operations: 39.0ms
ival-mult: 17.0ms (43.1% of total)
ival-div: 9.0ms (22.8% of total)
ival-fabs: 4.0ms (10.1% of total)
ival-sqrt: 4.0ms (10.1% of total)
ival-add: 2.0ms (5.1% of total)
ival-sub: 2.0ms (5.1% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series40.0ms (0.8%)

Memory
-13.0MiB live, 38.4MiB allocated
Counts
18 → 52
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))
(fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a)))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (/.f64 b a) a)
(*.f64 a a)
(/.f64 (+.f64 b a) a)
Outputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (pow a 2)) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(fabs (/ (* (+ a b) (- a b)) (pow a 2)))
(sqrt (fabs (/ (* (+ a b) (- a b)) (pow a 2))))
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 (/ (pow b 2) a))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) a)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) a)
(/ b (pow a 2))
(pow a 2)
(/ b a)
(/ (+ a b) a)
-1
(- (/ (pow b 2) (pow a 2)) 1)
1
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
a
(* a (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* a (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(+ 1 (/ b a))
(+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))
(fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2))))
(sqrt (fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (* -1 (/ (+ b (* -1 b)) a)) 1)))
(* -1 (* a (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1)))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 (/ (pow b 2) a)))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* (pow b 2) (- (/ a (pow b 2)) (/ 1 a)))
(* b (+ (/ 1 a) (/ 1 b)))
(fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2)))
(sqrt (fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2))))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
Calls

6 calls:

TimeVariablePointExpression
25.0ms
a
@0
((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (* (- a b) (+ b a)) (* a a)) (fabs (/ (* (- a b) (+ b a)) (* a a))) (sqrt (fabs (/ (* (- a b) (+ b a)) (* a a)))) (* (- a b) (+ b a)) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (* a a) (/ (+ b a) a))
3.0ms
a
@-inf
((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (* (- a b) (+ b a)) (* a a)) (fabs (/ (* (- a b) (+ b a)) (* a a))) (sqrt (fabs (/ (* (- a b) (+ b a)) (* a a)))) (* (- a b) (+ b a)) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (* a a) (/ (+ b a) a))
3.0ms
b
@inf
((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (* (- a b) (+ b a)) (* a a)) (fabs (/ (* (- a b) (+ b a)) (* a a))) (sqrt (fabs (/ (* (- a b) (+ b a)) (* a a)))) (* (- a b) (+ b a)) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (* a a) (/ (+ b a) a))
2.0ms
b
@-inf
((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (* (- a b) (+ b a)) (* a a)) (fabs (/ (* (- a b) (+ b a)) (* a a))) (sqrt (fabs (/ (* (- a b) (+ b a)) (* a a)))) (* (- a b) (+ b a)) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (* a a) (/ (+ b a) a))
2.0ms
a
@inf
((sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs (+ (* (/ (/ b a) a) b) -1)) (+ (* (/ (/ b a) a) b) -1) (sqrt (fabs (/ (- (* a a) (* b b)) (* a a)))) (fabs (/ (- (* a a) (* b b)) (* a a))) (/ (- (* a a) (* b b)) (* a a)) (/ (* (- a b) (+ b a)) (* a a)) (fabs (/ (* (- a b) (+ b a)) (* a a))) (sqrt (fabs (/ (* (- a b) (+ b a)) (* a a)))) (* (- a b) (+ b a)) (* (/ (+ b a) a) (- a b)) (fabs (/ (* (/ (+ b a) a) (- a b)) a)) (sqrt (fabs (/ (* (/ (+ b a) a) (- a b)) a))) (/ (* (/ (+ b a) a) (- a b)) a) (/ (/ b a) a) (* a a) (/ (+ b a) a))

simplify190.0ms (3.9%)

Memory
10.8MiB live, 200.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0130500
1408395
21519383
08900370
Stop Event
1×iter limit
1×node limit
Counts
52 → 51
Calls
Call 1
Inputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (pow a 2)) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(fabs (/ (* (+ a b) (- a b)) (pow a 2)))
(sqrt (fabs (/ (* (+ a b) (- a b)) (pow a 2))))
(* -1 (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 (/ (pow b 2) a))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) a)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) a)
(/ b (pow a 2))
(pow a 2)
(/ b a)
(/ (+ a b) a)
-1
(- (/ (pow b 2) (pow a 2)) 1)
1
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
a
(* a (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* a (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(+ 1 (/ b a))
(+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))
(fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2))))
(sqrt (fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2)))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (* -1 (/ (+ b (* -1 b)) a)) 1)))
(* -1 (* a (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1)))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 (/ (pow b 2) a)))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* (pow b 2) (- (/ a (pow b 2)) (/ 1 a)))
(* b (+ (/ 1 a) (/ 1 b)))
(fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2)))
(sqrt (fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2))))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
Outputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(/ (pow b 2) (pow a 2))
(*.f64 (/.f64 b (*.f64 a a)) b)
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))
(* -1 (/ (pow b 2) (pow a 2)))
(*.f64 (/.f64 (/.f64 (neg.f64 b) a) a) b)
(/ (+ (* -1 (pow b 2)) (pow a 2)) (pow a 2))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(*.f64 (/.f64 (/.f64 (neg.f64 b) a) a) b)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(fabs (/ (* (+ a b) (- a b)) (pow a 2)))
(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(sqrt (fabs (/ (* (+ a b) (- a b)) (pow a 2))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(*.f64 (neg.f64 b) b)
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 (/ (pow b 2) a))
(*.f64 (/.f64 (neg.f64 b) a) b)
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) a)
(*.f64 (/.f64 (neg.f64 b) a) b)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) a)
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(/ b (pow a 2))
(/.f64 b (*.f64 a a))
(pow a 2)
(*.f64 a a)
(/ b a)
(/.f64 b a)
(/ (+ a b) a)
(/.f64 (+.f64 b a) a)
-1
#s(literal -1 binary64)
(- (/ (pow b 2) (pow a 2)) 1)
(fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))
1
#s(literal 1 binary64)
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(*.f64 (*.f64 a (-.f64 a b)) (/.f64 (+.f64 b a) a))
a
(* a (+ 1 (+ (* -1 (/ b a)) (/ b a))))
a
(* a (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(*.f64 (-.f64 a b) (/.f64 (+.f64 b a) a))
(+ 1 (/ b a))
(/.f64 (+.f64 b a) a)
(+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2))))
(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(sqrt (fabs (* -1 (/ (* (+ b (* -1 a)) (- b (* -1 a))) (pow a 2)))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(*.f64 (*.f64 a (-.f64 a b)) (/.f64 (+.f64 b a) a))
(* -1 (* a (- (* -1 (/ (+ b (* -1 b)) a)) 1)))
a
(* -1 (* a (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1)))
(*.f64 (-.f64 a b) (/.f64 (+.f64 b a) a))
(+ (* b (+ a (* -1 a))) (pow a 2))
(*.f64 a a)
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ a (* -1 (/ (pow b 2) a)))
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(*.f64 (-.f64 (/.f64 (/.f64 #s(literal 1 binary64) a) a) (/.f64 #s(literal 1 binary64) (*.f64 b b))) (*.f64 b b))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 b b)) (/.f64 (/.f64 #s(literal 1 binary64) a) a)) (*.f64 b b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(*.f64 (neg.f64 b) b)
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(*.f64 (*.f64 (fma.f64 (/.f64 a b) (/.f64 a b) #s(literal -1 binary64)) b) b)
(* (pow b 2) (- (/ a (pow b 2)) (/ 1 a)))
(*.f64 (-.f64 (/.f64 (/.f64 a b) b) (/.f64 #s(literal 1 binary64) a)) (*.f64 b b))
(* b (+ (/ 1 a) (/ 1 b)))
(/.f64 (+.f64 b a) a)
(fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2)))
(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(sqrt (fabs (/ (* (+ a (* -1 b)) (- a (* -1 b))) (pow a 2))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(*.f64 (neg.f64 b) b)
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(*.f64 (*.f64 (fma.f64 (/.f64 a b) (/.f64 a b) #s(literal -1 binary64)) b) b)

rewrite151.0ms (3.1%)

Memory
-14.2MiB live, 122.5MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030205
050201
1184179
21358140
09277140
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
18 → 1 485
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))
(fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64)))
#s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))
(/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))
(fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a)))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (/.f64 b a) a)
(*.f64 a a)
(/.f64 (+.f64 b a) a)
Outputs
(*.f64 (neg.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(*.f64 (fabs.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (fabs.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(*.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(*.f64 (pow.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64)) (pow.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))
(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (*.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b) (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b))) (+.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b)))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))) (-.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64)) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (fma.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (*.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b) (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b) (*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 (/.f64 (/.f64 b a) a)) b)))))
(/.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (*.f64 (neg.f64 b) (/.f64 (/.f64 b a) a)) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal -1 binary64) (*.f64 (neg.f64 b) (/.f64 (/.f64 b a) a))))))
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(fma.f64 (/.f64 (neg.f64 b) a) (/.f64 (-.f64 b a) (neg.f64 a)) (*.f64 (/.f64 (-.f64 b a) a) #s(literal 1 binary64)))
(fma.f64 (/.f64 (neg.f64 b) a) (/.f64 (neg.f64 b) a) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(fma.f64 (/.f64 (neg.f64 b) a) (/.f64 b a) #s(literal 1 binary64))
(fma.f64 (neg.f64 b) (/.f64 b (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(fma.f64 #s(literal 1 binary64) (/.f64 (-.f64 b a) a) (*.f64 (/.f64 (-.f64 b a) a) (/.f64 b a)))
(fma.f64 (/.f64 (/.f64 b a) a) b (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(fma.f64 (/.f64 b a) (/.f64 b (neg.f64 (neg.f64 a))) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(fma.f64 (/.f64 b a) (/.f64 (-.f64 b a) a) (*.f64 (/.f64 (-.f64 b a) a) #s(literal 1 binary64)))
(fma.f64 (/.f64 b a) (/.f64 (neg.f64 b) a) #s(literal 1 binary64))
(fma.f64 (/.f64 b a) (/.f64 b a) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(fma.f64 b (/.f64 (/.f64 b a) a) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(sqrt.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (*.f64 a a) a) (neg.f64 a)) (/.f64 (*.f64 (/.f64 b a) b) (neg.f64 a)))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (*.f64 (neg.f64 a) a)) (/.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (*.f64 (neg.f64 a) a)))
(-.f64 (/.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 (neg.f64 a) a)) (/.f64 (/.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 (neg.f64 a) a)))
(-.f64 (/.f64 (*.f64 (-.f64 b a) b) (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 (neg.f64 a) (-.f64 b a)) (*.f64 (neg.f64 a) a)))
(-.f64 (/.f64 (*.f64 (-.f64 b a) b) (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 (neg.f64 (-.f64 b a)) a) (*.f64 (neg.f64 a) a)))
(-.f64 (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 (neg.f64 (neg.f64 b)) b) (*.f64 (neg.f64 a) a)))
(-.f64 (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)) (*.f64 (/.f64 (neg.f64 b) a) (/.f64 b a)))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (*.f64 (fma.f64 b b (*.f64 a a)) (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (fma.f64 b b (*.f64 a a)) (*.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #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 a a))) (/.f64 (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 a a))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (*.f64 a a)) (/.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (*.f64 a a)))
(-.f64 (/.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 a a)) (/.f64 (/.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 a a)))
(-.f64 (*.f64 (/.f64 (-.f64 b a) a) (/.f64 b a)) (/.f64 (*.f64 (neg.f64 a) (-.f64 b a)) (*.f64 a a)))
(-.f64 (*.f64 (/.f64 (-.f64 b a) a) (/.f64 b a)) (/.f64 (*.f64 (neg.f64 (-.f64 b a)) a) (*.f64 a a)))
(-.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (neg.f64 b)) b) (*.f64 a a)))
(-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(fabs.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))))
(fabs.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(fabs.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(+.f64 (/.f64 (neg.f64 (*.f64 (-.f64 b a) b)) (*.f64 a a)) (/.f64 (neg.f64 (*.f64 (-.f64 b a) a)) (*.f64 a a)))
(+.f64 (/.f64 (*.f64 (neg.f64 a) a) (*.f64 a a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 (/.f64 b a) (-.f64 b a)) (neg.f64 a)) (/.f64 (*.f64 #s(literal 1 binary64) (-.f64 b a)) (neg.f64 a)))
(+.f64 (/.f64 (*.f64 (-.f64 b a) (/.f64 b a)) (neg.f64 a)) (/.f64 (*.f64 (-.f64 b a) #s(literal 1 binary64)) (neg.f64 a)))
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 b a) b) a) (neg.f64 a)) (/.f64 (/.f64 (*.f64 (-.f64 b a) a) a) (neg.f64 a)))
(+.f64 (/.f64 (*.f64 (-.f64 b a) a) (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 (-.f64 b a) b) (*.f64 (neg.f64 a) a)))
(+.f64 (/.f64 (*.f64 (/.f64 b a) (-.f64 b a)) a) (/.f64 (*.f64 #s(literal 1 binary64) (-.f64 b a)) a))
(+.f64 (/.f64 (*.f64 (-.f64 b a) (/.f64 b a)) a) (/.f64 (*.f64 (-.f64 b a) #s(literal 1 binary64)) a))
(+.f64 (/.f64 (/.f64 (*.f64 (-.f64 b a) b) a) a) (/.f64 (/.f64 (*.f64 (-.f64 b a) a) a) a))
(+.f64 (/.f64 (/.f64 (*.f64 a a) a) (neg.f64 a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 (-.f64 b a) b) (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 (-.f64 b a) a) (*.f64 (neg.f64 a) a)))
(+.f64 (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)) (/.f64 (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)) (*.f64 (neg.f64 a) a)))
(+.f64 (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (*.f64 (fma.f64 b b (*.f64 a a)) (*.f64 a a))) (/.f64 (*.f64 (*.f64 (neg.f64 b) b) (*.f64 b b)) (*.f64 (fma.f64 b b (*.f64 a a)) (*.f64 a a))))
(+.f64 (*.f64 (/.f64 (-.f64 b a) a) #s(literal 1 binary64)) (*.f64 (/.f64 (-.f64 b a) a) (/.f64 b a)))
(+.f64 (*.f64 (/.f64 (-.f64 b a) a) (/.f64 b a)) (*.f64 (/.f64 (-.f64 b a) a) #s(literal 1 binary64)))
(+.f64 (*.f64 (/.f64 (neg.f64 b) a) (/.f64 b a)) #s(literal 1 binary64))
(+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(+.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 (neg.f64 b) b) a) a))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)) (*.f64 a a)))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (neg.f64 b) a) (/.f64 b a)))
(/.f64 (neg.f64 (neg.f64 b)) (*.f64 a a))
(/.f64 (/.f64 (neg.f64 b) a) (neg.f64 (neg.f64 (neg.f64 a))))
(/.f64 (/.f64 (neg.f64 b) a) (neg.f64 a))
(/.f64 (neg.f64 b) (*.f64 (neg.f64 a) a))
(/.f64 (/.f64 b a) (neg.f64 (neg.f64 a)))
(/.f64 (/.f64 b a) a)
(/.f64 b (*.f64 a a))
(neg.f64 (/.f64 (/.f64 (neg.f64 b) a) a))
(sqrt.f64 (/.f64 (*.f64 b b) (pow.f64 a #s(literal 4 binary64))))
(fabs.f64 (/.f64 b (*.f64 (neg.f64 a) a)))
(fabs.f64 (/.f64 (/.f64 b a) a))
(*.f64 (neg.f64 (neg.f64 (neg.f64 a))) (neg.f64 (neg.f64 (neg.f64 a))))
(*.f64 (sqrt.f64 (*.f64 (neg.f64 a) a)) (sqrt.f64 (*.f64 (neg.f64 a) a)))
(*.f64 (sqrt.f64 (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 (neg.f64 a)))
(*.f64 (sqrt.f64 (pow.f64 a #s(literal 3 binary64))) (sqrt.f64 a))
(*.f64 (sqrt.f64 (neg.f64 a)) (sqrt.f64 (pow.f64 a #s(literal 3 binary64))))
(*.f64 (sqrt.f64 a) (sqrt.f64 (pow.f64 a #s(literal 3 binary64))))
(*.f64 (exp.f64 (log.f64 a)) (exp.f64 (log.f64 a)))
(*.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 a a)
(pow.f64 (exp.f64 (log.f64 a)) #s(literal 2 binary64))
(pow.f64 (neg.f64 (neg.f64 a)) #s(literal 2 binary64))
(pow.f64 (pow.f64 a #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 a) a))
(sqrt.f64 (pow.f64 a #s(literal 4 binary64)))
(fabs.f64 (*.f64 (neg.f64 a) a))
(fabs.f64 (*.f64 a a))
(exp.f64 (*.f64 (log.f64 (neg.f64 a)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 a) #s(literal 2 binary64))) (sinh.f64 (*.f64 (log.f64 a) #s(literal 2 binary64))))
(*.f64 (/.f64 (+.f64 (neg.f64 b) a) (-.f64 b a)) (/.f64 (-.f64 (neg.f64 b) a) a))
(*.f64 (/.f64 (+.f64 b (neg.f64 a)) (-.f64 b a)) (/.f64 (-.f64 b (neg.f64 a)) a))
(*.f64 (/.f64 (+.f64 b a) (-.f64 b a)) (/.f64 (-.f64 b a) a))
(*.f64 (/.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) (fma.f64 (-.f64 b a) a (*.f64 b b))) (/.f64 (+.f64 b a) a))
(/.f64 (+.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 3 binary64))) (+.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (*.f64 #s(literal 1 binary64) (/.f64 b a)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 b a) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 b) a (*.f64 (neg.f64 a) a))) (*.f64 a a))
(/.f64 (neg.f64 (fma.f64 b a (*.f64 a a))) (*.f64 (neg.f64 a) a))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))) (neg.f64 (-.f64 (/.f64 b a) #s(literal 1 binary64))))
(/.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 b a) #s(literal 1 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (neg.f64 (*.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) a)))
(/.f64 (fma.f64 (neg.f64 b) a (*.f64 (neg.f64 a) a)) (*.f64 (neg.f64 a) a))
(/.f64 (fma.f64 b a (*.f64 a a)) (*.f64 a a))
(/.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 b a) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) a))
(/.f64 (-.f64 #s(literal 1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (/.f64 (-.f64 b a) a))
(/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (neg.f64 (*.f64 (-.f64 b a) a)))
(/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 (-.f64 b a) a))
(/.f64 (+.f64 b a) (neg.f64 (neg.f64 (neg.f64 a))))
(/.f64 (+.f64 b a) (neg.f64 (neg.f64 a)))
(/.f64 (+.f64 b a) (neg.f64 a))
(/.f64 (+.f64 b a) a)
(neg.f64 (/.f64 (+.f64 b a) a))
(-.f64 (/.f64 (/.f64 (*.f64 b b) (-.f64 b a)) (neg.f64 a)) (/.f64 (/.f64 (*.f64 a a) (-.f64 b a)) (neg.f64 a)))
(-.f64 (/.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (/.f64 b a) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 b a) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 b b) (*.f64 (-.f64 b a) a)) (/.f64 (*.f64 a a) (*.f64 (-.f64 b a) a)))
(-.f64 (/.f64 (/.f64 (*.f64 b b) (-.f64 b a)) a) (/.f64 (/.f64 (*.f64 a a) (-.f64 b a)) a))
(+.f64 (/.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 b a) a (*.f64 b b))) (neg.f64 a)) (/.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 b a) a (*.f64 b b))) (neg.f64 a)))
(+.f64 (/.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 b a) #s(literal 1 binary64))))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (*.f64 (/.f64 b a) #s(literal 1 binary64))))))
(+.f64 (/.f64 (*.f64 (neg.f64 b) a) (*.f64 (neg.f64 a) a)) #s(literal 1 binary64))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (*.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) a)) (/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) a)))
(+.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) a)) (/.f64 (pow.f64 a #s(literal 3 binary64)) (*.f64 (fma.f64 (-.f64 b a) a (*.f64 b b)) a)))
(+.f64 (/.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 b a) a (*.f64 b b))) a) (/.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 b a) a (*.f64 b b))) a))
(+.f64 (/.f64 (*.f64 b a) (*.f64 a a)) #s(literal 1 binary64))
(+.f64 (/.f64 (*.f64 b b) (*.f64 (-.f64 b a) a)) (/.f64 (*.f64 (neg.f64 a) a) (*.f64 (-.f64 b a) a)))
(+.f64 (/.f64 (neg.f64 a) a) (/.f64 (neg.f64 b) a))
(+.f64 (/.f64 a (neg.f64 a)) (/.f64 (neg.f64 b) a))
(+.f64 (/.f64 (neg.f64 b) a) (/.f64 (neg.f64 a) a))
(+.f64 (/.f64 (neg.f64 b) a) (/.f64 a (neg.f64 a)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))
(+.f64 (/.f64 b a) #s(literal 1 binary64))

eval108.0ms (2.2%)

Memory
-10.4MiB live, 130.9MiB allocated
Compiler

Compiled 20 750 to 3 605 computations (82.6% saved)

prune11.0ms (0.2%)

Memory
33.9MiB live, 33.9MiB allocated
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New7752777
Fresh000
Picked224
Done000
Total7774781
Accuracy
100.0%
Counts
781 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓100.0%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
▶80.7%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
▶98.1%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
Compiler

Compiled 74 to 47 computations (36.5% saved)

simplify125.0ms (2.5%)

Memory
-7.9MiB live, 90.8MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 6 expressions of interest:

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

Useful iterations: 2 (0.0ms)

IterNodesCost
017103
024103
15695
224491
3162491
0908391
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
(/.f64 b (*.f64 a a))
b
(*.f64 a a)
a
#s(literal -1 binary64)
Outputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))
#s(literal 1 binary64)
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
(/.f64 b (*.f64 a a))
b
(*.f64 a a)
a
#s(literal -1 binary64)

localize32.0ms (0.6%)

Memory
-13.9MiB live, 32.2MiB allocated
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
accuracy0.0
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
accuracy0.00390625
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
accuracy13.112333262444968
(/.f64 b (*.f64 a a))
accuracy0.00390625
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
accuracy1.2582199636917244
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))
Samples
24.0ms256×0valid
Compiler

Compiled 83 to 16 computations (80.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 14.0ms
ival-mult: 5.0ms (34.7% of total)
ival-div: 3.0ms (20.8% of total)
ival-fabs: 2.0ms (13.9% of total)
ival-sqrt: 2.0ms (13.9% of total)
ival-add: 1.0ms (6.9% of total)
ival-sub: 1.0ms (6.9% of total)
ival-assert: 0.0ms (0% of total)
ival-true: 0.0ms (0% of total)
exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory
4.1MiB live, 4.1MiB allocated
Counts
7 → 9
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
(/.f64 b (*.f64 a a))
Outputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(/ b (pow a 2))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
Calls

6 calls:

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

simplify89.0ms (1.8%)

Memory
14.8MiB live, 61.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02283
14477
212777
349677
4474777
0817072
Stop Event
1×iter limit
1×node limit
Counts
9 → 9
Calls
Call 1
Inputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(/ (pow b 2) (pow a 2))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(/ b (pow a 2))
-1
(- (/ (pow b 2) (pow a 2)) 1)
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
Outputs
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
(fabs (- (/ (pow b 2) (pow a 2)) 1))
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
(/ (pow b 2) (pow a 2))
(*.f64 (/.f64 b a) (/.f64 b a))
(/ (+ (* -1 (pow a 2)) (pow b 2)) (pow a 2))
(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
(/ b (pow a 2))
(/.f64 b (*.f64 a a))
-1
#s(literal -1 binary64)
(- (/ (pow b 2) (pow a 2)) 1)
(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
(* (pow b 2) (- (/ 1 (pow a 2)) (/ 1 (pow b 2))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 a a)) (/.f64 #s(literal 1 binary64) (*.f64 b b))) (*.f64 b b))

rewrite117.0ms (2.4%)

Memory
7.5MiB live, 54.6MiB allocated
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01796
02495
19687
276969
0959469
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
7 → 410
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))))
(fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))
(fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64))
(/.f64 b (*.f64 a a))
Outputs
(*.f64 (neg.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))) #s(literal 1/2 binary64))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64))
(*.f64 (neg.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (neg.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (fabs.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64))) (fabs.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64))))
(*.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))) #s(literal 1/2 binary64)))
(+.f64 (cosh.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (sinh.f64 (*.f64 (log.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))) #s(literal 1/2 binary64))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (+.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)) (-.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/4 binary64)))
(*.f64 (/.f64 (fma.f64 b b (*.f64 a a)) (fma.f64 b b (*.f64 a a))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (/.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(*.f64 (/.f64 (+.f64 (neg.f64 a) b) (neg.f64 a)) (/.f64 (-.f64 (neg.f64 a) b) a))
(*.f64 (/.f64 (+.f64 (neg.f64 a) b) (neg.f64 a)) (/.f64 (-.f64 (neg.f64 a) b) (neg.f64 a)))
(*.f64 (/.f64 (+.f64 (neg.f64 a) b) a) (/.f64 (-.f64 (neg.f64 a) b) a))
(*.f64 (/.f64 (+.f64 (neg.f64 a) b) a) (/.f64 (-.f64 (neg.f64 a) b) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) (neg.f64 a)) (/.f64 (fabs.f64 (-.f64 b a)) (neg.f64 a)))
(*.f64 (/.f64 (fabs.f64 (+.f64 b a)) a) (/.f64 (fabs.f64 (-.f64 b a)) a))
(*.f64 (neg.f64 (/.f64 (hypot.f64 b a) a)) (neg.f64 (/.f64 (hypot.f64 b a) a)))
(*.f64 (fabs.f64 (/.f64 (hypot.f64 b a) a)) (fabs.f64 (/.f64 (hypot.f64 b a) a)))
(*.f64 (fabs.f64 (/.f64 (+.f64 b a) a)) (fabs.f64 (/.f64 (-.f64 a b) a)))
(*.f64 (/.f64 (-.f64 a b) a) (/.f64 (+.f64 b a) a))
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 (/.f64 b a) #s(literal 1 binary64)))
(*.f64 (/.f64 (+.f64 b a) a) (/.f64 (-.f64 a b) a))
(*.f64 (fabs.f64 (+.f64 b a)) (fabs.f64 (/.f64 (-.f64 a b) (*.f64 a a))))
(*.f64 (/.f64 (hypot.f64 b a) a) (/.f64 (hypot.f64 b a) a))
(*.f64 (+.f64 b a) (/.f64 (-.f64 a b) (*.f64 a a)))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)))
(pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64))
(pow.f64 (pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (/.f64 (hypot.f64 b a) a) #s(literal 2 binary64)) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal 1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(/.f64 (*.f64 #s(literal -1 binary64) (neg.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64))))) (neg.f64 (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) (neg.f64 a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))))
(/.f64 (*.f64 #s(literal -1 binary64) (-.f64 #s(literal -1 binary64) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)))) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)))) (*.f64 (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64)))) (+.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))) (pow.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1 binary64))))
(/.f64 (-.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))))) (-.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)))))
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(+.f64 (*.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64)) (*.f64 (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) #s(literal -1 binary64)))
(+.f64 (*.f64 #s(literal -1 binary64) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))) (*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(+.f64 (neg.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))) (neg.f64 (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(+.f64 (/.f64 (*.f64 (neg.f64 a) a) (*.f64 a a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (neg.f64 (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))) (/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(+.f64 (/.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (neg.f64 (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64))))))
(+.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))))
(+.f64 (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (+.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))))))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (*.f64 (*.f64 (fma.f64 b b (*.f64 a a)) a) a)) (/.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (*.f64 (fma.f64 b b (*.f64 a a)) a) a)))
(+.f64 (/.f64 (/.f64 (*.f64 a a) a) (neg.f64 a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(+.f64 (/.f64 (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 3 binary64)) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))) (/.f64 #s(literal -1 binary64) (-.f64 (-.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64))) (pow.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 2 binary64)))))
(+.f64 (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))) #s(literal 1 binary64))
(+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (*.f64 a a) (*.f64 (neg.f64 a) a)))
(+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal -1 binary64))
(+.f64 #s(literal -1 binary64) (pow.f64 (/.f64 b a) #s(literal 2 binary64)))
(+.f64 #s(literal 1 binary64) (neg.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64))))
(/.f64 (/.f64 (neg.f64 b) a) (neg.f64 a))
(/.f64 (/.f64 b a) a)
(/.f64 (neg.f64 b) (*.f64 (neg.f64 a) a))
(/.f64 b (*.f64 a a))
(neg.f64 (/.f64 (/.f64 (neg.f64 b) a) a))
(sqrt.f64 (/.f64 (*.f64 b b) (pow.f64 a #s(literal 4 binary64))))
(fabs.f64 (/.f64 (/.f64 (neg.f64 b) a) a))
(fabs.f64 (/.f64 b (*.f64 a a)))

eval59.0ms (1.2%)

Memory
-20.3MiB live, 31.9MiB allocated
Compiler

Compiled 7 797 to 941 computations (87.9% saved)

prune4.0ms (0.1%)

Memory
10.0MiB live, 10.0MiB allocated
Pruning

4 alts after pruning (1 fresh and 3 done)

PrunedKeptTotal
New2271228
Fresh000
Picked022
Done112
Total2284232
Accuracy
100.0%
Counts
232 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓100.0%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
✓80.7%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
✓98.1%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
Compiler

Compiled 86 to 52 computations (39.5% saved)

simplify128.0ms (2.6%)

Memory
-29.9MiB live, 62.3MiB allocated
Algorithm
1×egg-herbie
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
cost-diff0
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
cost-diff0
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
cost-diff0
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
cost-diff2
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01482
02082
15172
223872
3161170
0981068
Stop Event
1×iter limit
1×node limit
1×iter limit
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(/.f64 (+.f64 b a) a)
(+.f64 b a)
b
a
(-.f64 a b)
Outputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (neg.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (neg.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(neg.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(/.f64 (+.f64 b a) a)
(+.f64 b a)
b
a
(-.f64 a b)

localize30.0ms (0.6%)

Memory
24.0MiB live, 24.0MiB allocated
Localize:

Found 4 expressions of interest:

NewMetricScoreProgram
accuracy0.00390625
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
accuracy0.01953125
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
accuracy0.03125
(/.f64 (+.f64 b a) a)
accuracy0.0546875
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
Samples
22.0ms256×0valid
Compiler

Compiled 60 to 15 computations (75% saved)

Precisions
Click to see histograms. Total time spent on operations: 15.0ms
ival-mult: 5.0ms (32.6% of total)
ival-div: 4.0ms (26.1% of total)
ival-sub: 2.0ms (13% of total)
ival-sqrt: 2.0ms (13% of total)
ival-add: 1.0ms (6.5% of total)
ival-fabs: 1.0ms (6.5% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory
3.3MiB live, 3.3MiB allocated
Counts
5 → 25
Calls
Call 1
Inputs
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (+.f64 b a) a)
Outputs
(* -1 (/ (pow b 2) a))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) a)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) a)
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(/ b a)
(/ (+ a b) a)
a
(* a (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* a (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
1
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
(+ 1 (/ b a))
(* -1 (* a (- (* -1 (/ (+ b (* -1 b)) a)) 1)))
(* -1 (* a (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1)))
(+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))
(+ a (* -1 (/ (pow b 2) a)))
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(* (pow b 2) (- (/ a (pow b 2)) (/ 1 a)))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* b (+ (/ 1 a) (/ 1 b)))
Calls

6 calls:

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

simplify195.0ms (4%)

Memory
-15.3MiB live, 79.5MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069224
1220164
2787164
34029164
08478162
Stop Event
1×iter limit
1×node limit
Counts
25 → 24
Calls
Call 1
Inputs
(* -1 (/ (pow b 2) a))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) a)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) a)
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(* -1 (/ (pow b 2) (pow a 2)))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(/ b a)
(/ (+ a b) a)
a
(* a (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* a (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
1
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
(+ 1 (/ b a))
(* -1 (* a (- (* -1 (/ (+ b (* -1 b)) a)) 1)))
(* -1 (* a (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1)))
(+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))
(+ a (* -1 (/ (pow b 2) a)))
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(* (pow b 2) (- (/ a (pow b 2)) (/ 1 a)))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(* b (+ (/ 1 a) (/ 1 b)))
Outputs
(* -1 (/ (pow b 2) a))
(*.f64 (/.f64 (neg.f64 b) a) b)
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) a)
(*.f64 (/.f64 (neg.f64 b) a) b)
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) a)
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(sqrt (fabs (/ (- (pow a 2) (pow b 2)) (pow a 2))))
(sqrt.f64 (fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64))))
(fabs (/ (- (pow a 2) (pow b 2)) (pow a 2)))
(fabs.f64 (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))
(* -1 (/ (pow b 2) (pow a 2)))
(*.f64 (/.f64 (/.f64 b a) a) (neg.f64 b))
(/ (+ (* -1 (pow b 2)) (* a (+ b (* -1 b)))) (pow a 2))
(*.f64 (/.f64 (/.f64 b a) a) (neg.f64 b))
(/ (+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b))))) (pow a 2))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(/ b a)
(/.f64 b a)
(/ (+ a b) a)
(/.f64 (+.f64 a b) a)
a
(* a (+ 1 (+ (* -1 (/ b a)) (/ b a))))
a
(* a (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(fma.f64 (/.f64 (neg.f64 b) a) b a)
1
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ b a)) (/ b a)))
#s(literal 1 binary64)
(+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a))))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(+ 1 (/ b a))
(/.f64 (+.f64 a b) a)
(* -1 (* a (- (* -1 (/ (+ b (* -1 b)) a)) 1)))
a
(* -1 (* a (- (* -1 (/ (+ b (+ (* -1 b) (* -1 (/ (pow b 2) a)))) a)) 1)))
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a)))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(+ a (* -1 (/ (pow b 2) a)))
(fma.f64 (/.f64 (neg.f64 b) a) b a)
(+ 1 (* -1 (/ (pow b 2) (pow a 2))))
(/.f64 (fma.f64 (/.f64 (neg.f64 b) a) b a) a)
(* (pow b 2) (- (/ a (pow b 2)) (/ 1 a)))
(*.f64 (-.f64 (/.f64 a (*.f64 b b)) (/.f64 #s(literal 1 binary64) a)) (*.f64 b b))
(* (pow b 2) (- (/ 1 (pow b 2)) (/ 1 (pow a 2))))
(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) (*.f64 b b)) (/.f64 (/.f64 #s(literal 1 binary64) a) a)) (*.f64 b b))
(* b (+ (/ 1 a) (/ 1 b)))
(/.f64 (+.f64 a b) a)

rewrite96.0ms (2%)

Memory
4.5MiB live, 50.3MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01474
02074
19564
288352
0998151
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
5 → 282
Calls
Call 1
Inputs
(*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
#s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a))
(/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)
(/.f64 (+.f64 b a) a)
Outputs
(*.f64 (*.f64 (/.f64 (-.f64 a b) a) (/.f64 (fma.f64 a a (*.f64 b b)) (fma.f64 a a (*.f64 b b)))) (-.f64 a b))
(*.f64 (*.f64 (/.f64 (-.f64 a b) a) (/.f64 (fma.f64 a a (*.f64 b b)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (fma.f64 a (-.f64 a b) (*.f64 b b)))
(*.f64 (/.f64 (-.f64 (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64)))) (/.f64 (fma.f64 a a (*.f64 b b)) a))
(*.f64 (/.f64 (fma.f64 a a (*.f64 b b)) (fma.f64 a a (*.f64 b b))) (/.f64 (fma.f64 a a (*.f64 b b)) a))
(*.f64 (/.f64 (fma.f64 a a (*.f64 b b)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) (/.f64 (-.f64 a b) a)))
(*.f64 (/.f64 (-.f64 a b) a) (-.f64 a b))
(*.f64 (/.f64 (fma.f64 a a (*.f64 b b)) a) (/.f64 (-.f64 a b) (-.f64 a b)))
(*.f64 (-.f64 a b) (/.f64 (-.f64 a b) a))
(/.f64 (*.f64 (/.f64 (-.f64 a b) a) (fma.f64 a a (*.f64 b b))) (-.f64 a b))
(/.f64 (*.f64 (fma.f64 a a (*.f64 b b)) (/.f64 (-.f64 a b) a)) (-.f64 a b))
(/.f64 (*.f64 (-.f64 a b) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (neg.f64 (*.f64 (neg.f64 a) (fma.f64 a (-.f64 a b) (*.f64 b b)))))
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(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64))) (-.f64 (/.f64 b a) #s(literal 1 binary64)))
(/.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) #s(literal 1 binary64)) (neg.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (-.f64 a b) a))))
(/.f64 (+.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) #s(literal 1 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (-.f64 a b) a)))
(/.f64 (*.f64 (neg.f64 a) (-.f64 a b)) (*.f64 (neg.f64 a) a))
(/.f64 (*.f64 (neg.f64 a) (-.f64 a b)) (*.f64 a a))
(/.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) (neg.f64 (-.f64 (/.f64 b a) #s(literal 1 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) #s(literal 1 binary64)) (-.f64 (/.f64 b a) #s(literal 1 binary64)))
(/.f64 (*.f64 a (-.f64 a b)) (*.f64 (neg.f64 a) a))
(/.f64 (*.f64 a (-.f64 a b)) (*.f64 a a))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) (neg.f64 a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a))
(/.f64 (pow.f64 (/.f64 (-.f64 a b) a) #s(literal 2 binary64)) (/.f64 (-.f64 a b) a))
(/.f64 (fma.f64 a a (*.f64 b b)) (*.f64 (-.f64 a b) (neg.f64 a)))
(/.f64 (fma.f64 a a (*.f64 b b)) (*.f64 (-.f64 a b) a))
(/.f64 (-.f64 a b) (neg.f64 a))
(/.f64 (-.f64 a b) a)
(neg.f64 (/.f64 (-.f64 a b) a))
(fma.f64 (/.f64 b a) #s(literal 1 binary64) #s(literal 1 binary64))
(-.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a)) (/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a)))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) a) (/.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) a))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) (neg.f64 a)) (/.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) (neg.f64 a)))
(-.f64 (/.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (-.f64 (/.f64 b a) #s(literal 1 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (/.f64 b a) #s(literal 1 binary64))))
(-.f64 (/.f64 (*.f64 b b) (*.f64 (-.f64 a b) a)) (/.f64 (*.f64 a a) (*.f64 (-.f64 a b) a)))
(-.f64 (/.f64 (/.f64 (*.f64 b b) (-.f64 a b)) (neg.f64 a)) (/.f64 (/.f64 (*.f64 a a) (-.f64 a b)) (neg.f64 a)))
(-.f64 (/.f64 (/.f64 (*.f64 a a) (-.f64 a b)) (neg.f64 a)) (/.f64 (/.f64 (*.f64 b b) (-.f64 a b)) (neg.f64 a)))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 a a (*.f64 b b))) (*.f64 (-.f64 a b) a)) (/.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 a a (*.f64 b b))) (*.f64 (-.f64 a b) a)))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64)))) (*.f64 (-.f64 a b) a)) (/.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64)))) (*.f64 (-.f64 a b) a)))
(-.f64 (/.f64 (*.f64 a a) (*.f64 (-.f64 a b) a)) (/.f64 (*.f64 b b) (*.f64 (-.f64 a b) a)))
(-.f64 (/.f64 (/.f64 (*.f64 b b) (-.f64 a b)) a) (/.f64 (/.f64 (*.f64 a a) (-.f64 a b)) a))
(-.f64 (/.f64 (/.f64 (*.f64 a a) (-.f64 a b)) a) (/.f64 (/.f64 (*.f64 b b) (-.f64 a b)) a))
(-.f64 #s(literal -1 binary64) (/.f64 (neg.f64 b) a))
(-.f64 #s(literal 1 binary64) (/.f64 b a))
(+.f64 (/.f64 (pow.f64 (/.f64 b a) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (-.f64 a b) a))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (/.f64 b a) #s(literal 2 binary64)) (/.f64 (-.f64 a b) a))))
(+.f64 (/.f64 (*.f64 a b) (*.f64 a a)) #s(literal 1 binary64))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a)) (/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a)))
(+.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a)) (/.f64 (pow.f64 a #s(literal 3 binary64)) (*.f64 (fma.f64 a (-.f64 a b) (*.f64 b b)) a)))
(+.f64 (/.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) a) (/.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) a))
(+.f64 (/.f64 (*.f64 (neg.f64 b) b) (*.f64 (-.f64 a b) a)) (/.f64 (*.f64 a a) (*.f64 (-.f64 a b) a)))
(+.f64 (/.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) (neg.f64 a)) (/.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a (-.f64 a b) (*.f64 b b))) (neg.f64 a)))
(+.f64 (/.f64 (*.f64 b b) (*.f64 (-.f64 a b) a)) (/.f64 (*.f64 (neg.f64 a) a) (*.f64 (-.f64 a b) a)))
(+.f64 (/.f64 (/.f64 (*.f64 a a) (-.f64 a b)) (neg.f64 a)) (/.f64 (/.f64 (*.f64 b b) (-.f64 a b)) (neg.f64 a)))
(+.f64 (/.f64 (*.f64 a a) (*.f64 (-.f64 a b) a)) (/.f64 (*.f64 (neg.f64 b) b) (*.f64 (-.f64 a b) a)))
(+.f64 (/.f64 (/.f64 (*.f64 a a) (-.f64 a b)) a) (/.f64 (/.f64 (*.f64 b b) (-.f64 a b)) a))
(+.f64 #s(literal -1 binary64) (/.f64 (neg.f64 b) a))
(+.f64 (/.f64 (neg.f64 b) a) #s(literal -1 binary64))
(+.f64 (/.f64 b a) #s(literal 1 binary64))
(+.f64 #s(literal 1 binary64) (*.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (/.f64 b a))

eval44.0ms (0.9%)

Memory
-13.2MiB live, 32.4MiB allocated
Compiler

Compiled 10 352 to 1 411 computations (86.4% saved)

prune6.0ms (0.1%)

Memory
14.9MiB live, 14.9MiB allocated
Pruning

4 alts after pruning (0 fresh and 4 done)

PrunedKeptTotal
New2940294
Fresh000
Picked011
Done033
Total2944298
Accuracy
100.0%
Counts
298 → 4
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
✓100.0%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
✓80.7%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
✓98.1%
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
Compiler

Compiled 226 to 96 computations (57.5% saved)

regimes15.0ms (0.3%)

Memory
18.7MiB live, 18.7MiB allocated
Counts
8 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (/.f64 (+.f64 b a) a) (-.f64 a b)) a)))
Outputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
Calls

7 calls:

3.0ms
b
2.0ms
a
2.0ms
(*.f64 a a)
2.0ms
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
2.0ms
(*.f64 b b)
Results
AccuracySegmentsBranch
100.0%1(*.f64 b b)
100.0%1(*.f64 a a)
100.0%1(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
100.0%1(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
100.0%1(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
100.0%1a
100.0%1b
Compiler

Compiled 44 to 31 computations (29.5% saved)

regimes19.0ms (0.4%)

Memory
-32.5MiB live, 14.6MiB allocated
Accuracy

Total -12.5b remaining (-1024.5%)

Threshold costs -12.5b (-1024.5%)

Counts
4 → 1
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
(sqrt.f64 (fabs.f64 #s(approx (/ (- (* a a) (* b b)) (* a a)) #s(literal 1 binary64))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 b (*.f64 a a)) b #s(literal -1 binary64)))))
(sqrt.f64 (fabs.f64 (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (*.f64 a a))))
Outputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
Calls

7 calls:

10.0ms
(*.f64 a a)
2.0ms
a
2.0ms
b
1.0ms
(*.f64 b b)
1.0ms
(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
Results
AccuracySegmentsBranch
98.1%1(*.f64 b b)
98.1%1(*.f64 a a)
98.1%1(/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))
98.1%1(fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a)))
98.1%1(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (*.f64 a a))))
98.1%1a
98.1%1b
Compiler

Compiled 44 to 31 computations (29.5% saved)

simplify35.0ms (0.7%)

Memory
30.2MiB live, 30.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01738
14434
221634
3145234
Stop Event
1×node limit
Calls
Call 1
Inputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))
Outputs
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) (fabs.f64 (fma.f64 (/.f64 (/.f64 b a) a) b #s(literal -1 binary64)))))
(sqrt.f64 #s(approx (fabs (/ (- (* a a) (* b b)) (* a a))) #s(literal 1 binary64)))

soundness344.0ms (7%)

Memory
-26.2MiB live, 162.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030205
050201
1184179
21358140
09277140
025117
158104
2194104
31182104
45531104
08296101
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×node limit
1×iter limit
Compiler

Compiled 70 to 35 computations (50% saved)

preprocess19.0ms (0.4%)

Memory
28.4MiB live, 28.4MiB allocated
Remove

(abs a)

(abs b)

Compiler

Compiled 194 to 106 computations (45.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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