Difference of squares

Time bar (total: 2.1s)

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated; 0ms collecting garbage
Algorithm
1×search
Search
ProbabilityValidUnknownPreconditionInfiniteDomainCan'tIter
0%0%99.9%0.1%0%0%0%0
100%99.9%0%0.1%0%0%0%1
Compiler

Compiled 9 to 7 computations (22.2% saved)

sample597.0ms (28.6%)

Memory
10.9MiB live, 630.6MiB allocated; 124ms collecting garbage
Samples
377.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 191.0ms
ival-mult: 148.0ms (77.4% of total)
ival-sub: 33.0ms (17.2% of total)
ival-true: 5.0ms (2.6% of total)
ival-assert: 3.0ms (1.6% of total)
adjust: 2.0ms (1% of total)
Bogosity

explain64.0ms (3.1%)

Memory
0.0MiB live, 45.7MiB allocated; 10ms collecting garbage
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
140-0-(-.f64 (*.f64 a a) (*.f64 b b))
00-0-(*.f64 a a)
00-0-a
00-0-b
00-0-(*.f64 b b)
Explanations
Click to see full explanations table
OperatorSubexpressionExplanationCount
-.f64(-.f64 (*.f64 a a) (*.f64 b b))nan-rescue140
↳(*.f64 a a)overflow70
↳(*.f64 b b)overflow47
Confusion
Predicted +Predicted -
+140
-0242
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+1400
-00242
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0242
114
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
31.0ms512×0valid
Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions
Click to see histograms. Total time spent on operations: 19.0ms
ival-mult: 17.0ms (87.8% of total)
ival-sub: 2.0ms (10.3% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess134.0ms (6.4%)

Memory
-23.1MiB live, 24.0MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01338
14835
221535
337135
490935
5192335
6292635
7326935
8334735
9334735
10354635
057
087
1217
2817
32237
44037
58367
613857
720697
828987
932087
1032707
1132707
1233487
033487
Stop Event
1×iter limit
1×saturated
1×iter limit
1×saturated
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))
Symmetry

(abs b)

(abs a)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

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

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.3MiB live, 0.3MiB allocated; 0ms collecting garbage
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶94.5%
(-.f64 (*.f64 a a) (*.f64 b b))
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify116.0ms (5.6%)

Memory
-7.3MiB live, 40.0MiB allocated; 1ms collecting garbage
Localize:

Found 3 expressions of interest:

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

Useful iterations: 0 (0.0ms)

IterNodesCost
0515
0815
12115
28115
322315
440315
583615
6138515
7206915
8289815
9320815
10327015
11327015
12334815
0334815
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b
Outputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 a a)
a
(*.f64 b b)
b

localize15.0ms (0.7%)

Memory
7.3MiB live, 7.3MiB allocated; 0ms collecting garbage
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 b b)
accuracy0.0
(*.f64 a a)
accuracy3.152329300811441
(-.f64 (*.f64 a a) (*.f64 b b))
Samples
10.0ms256×0valid
Compiler

Compiled 17 to 7 computations (58.8% saved)

Precisions
Click to see histograms. Total time spent on operations: 4.0ms
ival-mult: 3.0ms (67.4% of total)
ival-sub: 1.0ms (22.5% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory
1.9MiB live, 1.9MiB allocated; 0ms collecting garbage
Counts
3 → 7
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 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)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Calls

6 calls:

TimeVariablePointExpression
1.0ms
a
@inf
((- (* a a) (* b b)) (* a a) (* b b))
1.0ms
a
@0
((- (* a a) (* b b)) (* a a) (* b b))
0.0ms
b
@inf
((- (* a a) (* b b)) (* a a) (* b b))
0.0ms
b
@-inf
((- (* a a) (* b b)) (* a a) (* b b))
0.0ms
a
@-inf
((- (* a a) (* b b)) (* a a) (* b b))

simplify155.0ms (7.5%)

Memory
-2.8MiB live, 94.1MiB allocated; 10ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01744
14044
215244
394344
4554144
0845843
Stop Event
1×iter limit
1×node limit
Counts
7 → 7
Calls
Call 1
Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 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)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(pow b 2)
(*.f64 b b)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (*.f64 b b))

rewrite62.0ms (3%)

Memory
1.3MiB live, 47.0MiB allocated; 7ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0513
0813
13713
032913
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
3 → 73
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
(*.f64 (+.f64 (neg.f64 a) (neg.f64 b)) (-.f64 (neg.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (neg.f64 a) (fabs.f64 b)) (-.f64 (neg.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (neg.f64 a) b) (-.f64 (neg.f64 a) b))
(*.f64 (+.f64 (fabs.f64 a) (neg.f64 b)) (-.f64 (fabs.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) (fabs.f64 b)) (-.f64 (fabs.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) b) (-.f64 (fabs.f64 a) b))
(*.f64 (+.f64 a (neg.f64 b)) (-.f64 a (neg.f64 b)))
(*.f64 (+.f64 a (fabs.f64 b)) (-.f64 a (fabs.f64 b)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(/.f64 (+.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 b) b) #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (*.f64 a a) (*.f64 (neg.f64 b) b)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (neg.f64 (fma.f64 b b (*.f64 a a))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (neg.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 b (neg.f64 b) (*.f64 a a))
(fma.f64 a a (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(fma.f64 a a (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) b))
(-.f64 (*.f64 a a) (*.f64 b b))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b)))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b)))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(*.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)))
(*.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)))
(*.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(*.f64 a a)
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 (fabs.f64 a) #s(literal 2 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 a) a))
(neg.f64 (*.f64 a (neg.f64 a)))
(fabs.f64 (*.f64 a a))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(*.f64 (pow.f64 b #s(literal 1 binary64)) (pow.f64 b #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 (fabs.f64 b)) (neg.f64 (fabs.f64 b)))
(*.f64 (fabs.f64 (fabs.f64 b)) (fabs.f64 (fabs.f64 b)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 (fabs.f64 b) (fabs.f64 b))
(*.f64 b b)
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (fabs.f64 b) #s(literal 2 binary64))
(pow.f64 b #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 b) b))
(fabs.f64 (*.f64 b b))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))

eval7.0ms (0.4%)

Memory
10.5MiB live, 10.5MiB allocated; 0ms collecting garbage
Compiler

Compiled 866 to 181 computations (79.1% saved)

prune3.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated; 0ms collecting garbage
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New76278
Fresh000
Picked101
Done000
Total77279
Accuracy
100.0%
Counts
79 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
▶49.1%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify69.0ms (3.3%)

Memory
10.9MiB live, 57.1MiB allocated; 3ms collecting garbage
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
cost-diff0
(+.f64 b a)
cost-diff0
(-.f64 a b)
cost-diff0
(*.f64 (-.f64 a b) (+.f64 b a))
cost-diff0
(neg.f64 b)
cost-diff0
(*.f64 (neg.f64 b) b)
cost-diff0
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01134
01634
13534
210134
324834
443134
586134
6139934
7208334
8291334
9322334
10328534
11328534
12336334
0336334
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
b
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
b
(+.f64 b a)
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
b
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(-.f64 a b)
a
b
(+.f64 b a)

localize34.0ms (1.6%)

Memory
-2.9MiB live, 49.4MiB allocated; 6ms collecting garbage
Localize:

Found 6 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(-.f64 a b)
accuracy0.0
(+.f64 b a)
accuracy0.0
(*.f64 (-.f64 a b) (+.f64 b a))
accuracy0.0
(*.f64 (neg.f64 b) b)
accuracy0.0
(neg.f64 b)
accuracy32.56734087821189
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Samples
27.0ms256×0valid
Compiler

Compiled 31 to 12 computations (61.3% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 6.0ms (55.5% of total)
ival-sub: 2.0ms (18.5% of total)
ival-add: 1.0ms (9.2% of total)
ival-neg: 1.0ms (9.2% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series6.0ms (0.3%)

Memory
7.8MiB live, 7.8MiB allocated; 0ms collecting garbage
Counts
6 → 31
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
b
(+ a b)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (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))))
(* a (+ 1 (/ b a)))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* b (- (/ a b) 1))
(* b (+ 1 (/ a b)))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
Calls

6 calls:

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

simplify170.0ms (8.1%)

Memory
-30.5MiB live, 204.9MiB allocated; 25ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092205
1299200
21122200
08075193
Stop Event
1×iter limit
1×node limit
Counts
31 → 29
Calls
Call 1
Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
b
(+ a b)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (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))))
(* a (+ 1 (/ b a)))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* b (- (/ a b) 1))
(* b (+ 1 (/ a b)))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (- (* -1 (/ a b)) 1)))
Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -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 b)
(neg.f64 b)
(- a b)
(-.f64 a b)
b
(+ a b)
(+.f64 b a)
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(*.f64 (neg.f64 (*.f64 a (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) 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 (neg.f64 (*.f64 a (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) a)
a
(* a (+ 1 (* -1 (/ b a))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 b a)) a)
(* a (+ 1 (/ b a)))
(fma.f64 (/.f64 b a) a a)
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(*.f64 (neg.f64 (*.f64 a (fma.f64 (/.f64 b a) (/.f64 b a) #s(literal -1 binary64)))) a)
(* -1 (* a (- (/ b a) 1)))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 b a)) a)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(fma.f64 (/.f64 b a) a a)
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 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 b))
(-.f64 a b)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (*.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 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (*.f64 b b))
(* b (- (/ a b) 1))
(*.f64 (-.f64 (/.f64 a b) #s(literal 1 binary64)) b)
(* b (+ 1 (/ a b)))
(fma.f64 (/.f64 a b) b b)
(* (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 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (*.f64 b b))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(*.f64 (-.f64 (/.f64 a b) #s(literal 1 binary64)) b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(fma.f64 (/.f64 a b) b b)

rewrite36.0ms (1.7%)

Memory
31.6MiB live, 31.6MiB allocated; 0ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01131
01631
16831
061031
Stop Event
1×iter limit
1×iter limit
1×node limit
1×iter limit
Counts
6 → 94
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
(+.f64 b a)
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b))
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b))
(*.f64 (fabs.f64 b) (neg.f64 (fabs.f64 b)))
(*.f64 (neg.f64 b) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 b) b)
(*.f64 b (neg.f64 b))
(neg.f64 (*.f64 b b))
(neg.f64 b)
(*.f64 (+.f64 (neg.f64 a) (fabs.f64 b)) (-.f64 (neg.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (neg.f64 a) (neg.f64 b)) (-.f64 (neg.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (neg.f64 a) b) (-.f64 (neg.f64 a) b))
(*.f64 (+.f64 (fabs.f64 a) (fabs.f64 b)) (-.f64 (fabs.f64 a) (fabs.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) (neg.f64 b)) (-.f64 (fabs.f64 a) (neg.f64 b)))
(*.f64 (+.f64 (fabs.f64 a) b) (-.f64 (fabs.f64 a) b))
(*.f64 (+.f64 a (fabs.f64 b)) (-.f64 a (fabs.f64 b)))
(*.f64 (+.f64 a (neg.f64 b)) (-.f64 a (neg.f64 b)))
(*.f64 (+.f64 b a) (-.f64 a b))
(*.f64 (-.f64 a b) (+.f64 b a))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (-.f64 a b)) (-.f64 b a))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b)) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 b a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 b a)) (+.f64 b a))
(/.f64 (*.f64 (+.f64 b a) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b (+.f64 b a) (*.f64 a a)))
(/.f64 (*.f64 (+.f64 b a) (*.f64 (+.f64 b a) (-.f64 a b))) (+.f64 b a))
(/.f64 (*.f64 (-.f64 a b) (*.f64 (+.f64 b a) (-.f64 b a))) (-.f64 b a))
(/.f64 (*.f64 (-.f64 a b) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(/.f64 (-.f64 (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b)) (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a))) (-.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a)))
(/.f64 (+.f64 (pow.f64 (*.f64 (-.f64 a b) b) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 a b) a) #s(literal 3 binary64))) (fma.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b) (-.f64 (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a)) (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a)))))
(/.f64 (+.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 (*.f64 (neg.f64 b) b) #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (*.f64 a a) (*.f64 (neg.f64 b) b)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (neg.f64 (fma.f64 b b (*.f64 a a))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (neg.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (-.f64 b a) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (*.f64 (+.f64 b a) (-.f64 a b))) (*.f64 (-.f64 b a) (+.f64 b a)))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (fma.f64 (-.f64 a b) a (*.f64 b b)) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (+.f64 b a) (-.f64 a b))) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (*.f64 (+.f64 b a) (-.f64 b a))) (*.f64 (fma.f64 b (+.f64 b a) (*.f64 a a)) (-.f64 b a)))
(/.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (fma.f64 b (+.f64 b a) (*.f64 a a)) (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (*.f64 (+.f64 b a) (-.f64 b a))) (*.f64 (+.f64 b a) (-.f64 b a)))
(/.f64 (*.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (+.f64 b a) (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))))
(fma.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 (fabs.f64 b)) (fabs.f64 b) (*.f64 a a))
(fma.f64 (neg.f64 (neg.f64 b)) (neg.f64 b) (*.f64 a a))
(fma.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)) (*.f64 (neg.f64 b) b))
(fma.f64 (neg.f64 a) (neg.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (fabs.f64 b) (neg.f64 (fabs.f64 b)) (*.f64 a a))
(fma.f64 (fabs.f64 a) (fabs.f64 a) (*.f64 (neg.f64 b) b))
(fma.f64 (-.f64 a b) b (*.f64 (-.f64 a b) a))
(fma.f64 (-.f64 a b) a (*.f64 (-.f64 a b) b))
(fma.f64 (neg.f64 b) (neg.f64 (neg.f64 b)) (*.f64 a a))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(fma.f64 b (-.f64 a b) (*.f64 (-.f64 a b) a))
(fma.f64 b (neg.f64 b) (*.f64 a a))
(fma.f64 a (-.f64 a b) (*.f64 (-.f64 a b) b))
(fma.f64 a a (*.f64 (neg.f64 b) b))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (*.f64 (-.f64 a b) b) (*.f64 (neg.f64 a) (-.f64 a b)))
(-.f64 (*.f64 (-.f64 a b) b) (*.f64 (neg.f64 (-.f64 a b)) a))
(-.f64 (*.f64 a a) (*.f64 (neg.f64 (neg.f64 b)) b))
(-.f64 (*.f64 a a) (*.f64 b b))
(+.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) b))
(+.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a))
(+.f64 (*.f64 (neg.f64 b) b) (*.f64 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (*.f64 (+.f64 b a) (-.f64 b a))) (-.f64 b a))
(*.f64 (/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(*.f64 (+.f64 b a) (/.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (-.f64 a b) (/.f64 (+.f64 b a) (+.f64 b a)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (neg.f64 (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (neg.f64 (*.f64 (+.f64 b a) (-.f64 a b))) (neg.f64 (+.f64 b a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (*.f64 (fma.f64 b b (*.f64 a a)) (+.f64 b a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b (+.f64 b a) (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (*.f64 (fma.f64 (*.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))) (+.f64 b a)))
(/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (+.f64 b a))
(-.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (*.f64 a a))) (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(-.f64 (/.f64 (*.f64 a a) (+.f64 b a)) (/.f64 (*.f64 b b) (+.f64 b a)))
(-.f64 a b)
(+.f64 (/.f64 (*.f64 (-.f64 a b) b) (+.f64 b a)) (/.f64 (*.f64 (-.f64 a b) a) (+.f64 b a)))
(+.f64 (/.f64 (*.f64 a a) (+.f64 b a)) (/.f64 (*.f64 (neg.f64 b) b) (+.f64 b a)))
(/.f64 (neg.f64 (*.f64 (+.f64 b a) (-.f64 b a))) (neg.f64 (-.f64 b a)))
(/.f64 (neg.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 a b) a (*.f64 b b))))
(/.f64 (*.f64 (+.f64 b a) (-.f64 b a)) (-.f64 b a))
(/.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 a a (-.f64 (*.f64 b b) (*.f64 b a))))
(/.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 (-.f64 a b) a (*.f64 b b)))
(/.f64 (*.f64 (+.f64 b a) (-.f64 a b)) (-.f64 a b))
(-.f64 (/.f64 (*.f64 b b) (-.f64 b a)) (/.f64 (*.f64 a a) (-.f64 b a)))
(+.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 a b) a (*.f64 b b))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 a b) a (*.f64 b b))))
(+.f64 b a)
(+.f64 a b)

eval40.0ms (1.9%)

Memory
-29.1MiB live, 18.0MiB allocated; 2ms collecting garbage
Compiler

Compiled 1 761 to 296 computations (83.2% saved)

prune3.0ms (0.1%)

Memory
6.9MiB live, 6.9MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1091110
Fresh000
Picked022
Done000
Total1093112
Accuracy
100.0%
Counts
112 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
✓49.1%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
▶59.4%
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify69.0ms (3.3%)

Memory
27.6MiB live, 73.9MiB allocated; 4ms collecting garbage
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
cost-diff0
(*.f64 a a)
cost-diff0
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0715
0815
12115
28115
322315
440115
582815
6137915
7206315
8290015
9321015
10327215
11327215
12335015
0335015
Stop Event
1×iter limit
1×saturated
1×iter limit
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a

localize62.0ms (3%)

Memory
-50.9MiB live, 29.5MiB allocated; 47ms collecting garbage
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 a a)
accuracy25.967843288910057
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Samples
58.0ms256×0valid
Compiler

Compiled 13 to 7 computations (46.2% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (66.3% of total)
ival-sub: 1.0ms (22.1% of total)
ival-true: 0.0ms (0% of total)
adjust: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0.1%)

Memory
5.9MiB live, 5.9MiB allocated; 0ms collecting garbage
Counts
2 → 6
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 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) (- (/ (pow a 2) (pow b 2)) 1))
Calls

6 calls:

TimeVariablePointExpression
0.0ms
a
@-inf
((- (* a a) (* b b)) (* a a))
0.0ms
a
@inf
((- (* a a) (* b b)) (* a a))
0.0ms
a
@0
((- (* a a) (* b b)) (* a a))
0.0ms
b
@inf
((- (* a a) (* b b)) (* a a))
0.0ms
b
@-inf
((- (* a a) (* b b)) (* a a))

simplify179.0ms (8.6%)

Memory
37.8MiB live, 256.6MiB allocated; 79ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01741
14041
215241
394341
4554141
0845840
Stop Event
1×iter limit
1×node limit
Counts
6 → 6
Calls
Call 1
Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 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) (- (/ (pow a 2) (pow b 2)) 1))
Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (*.f64 b b))

rewrite36.0ms (1.7%)

Memory
-10.9MiB live, 36.1MiB allocated; 2ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
0814
13714
032914
Stop Event
1×iter limit
1×iter limit
1×iter limit
1×unsound
1×iter limit
Counts
2 → 15
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 (pow.f64 a #s(literal 1 binary64)) (pow.f64 a #s(literal 1 binary64)))
(*.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 a)))
(*.f64 (neg.f64 (fabs.f64 a)) (neg.f64 (fabs.f64 a)))
(*.f64 (fabs.f64 (fabs.f64 a)) (fabs.f64 (fabs.f64 a)))
(*.f64 (neg.f64 a) (neg.f64 a))
(*.f64 (fabs.f64 a) (fabs.f64 a))
(*.f64 a a)
(pow.f64 (neg.f64 a) #s(literal 2 binary64))
(pow.f64 (fabs.f64 a) #s(literal 2 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 (neg.f64 a) a))
(neg.f64 (*.f64 a (neg.f64 a)))
(fabs.f64 (*.f64 a a))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))

eval2.0ms (0.1%)

Memory
4.8MiB live, 4.8MiB allocated; 0ms collecting garbage
Compiler

Compiled 256 to 59 computations (77% saved)

prune2.0ms (0.1%)

Memory
4.0MiB live, 4.0MiB allocated; 0ms collecting garbage
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New19019
Fresh000
Picked011
Done022
Total19322
Accuracy
100.0%
Counts
22 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
✓49.1%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
✓59.4%
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Compiler

Compiled 67 to 35 computations (47.8% saved)

regimes31.0ms (1.5%)

Memory
-25.9MiB live, 21.2MiB allocated; 2ms collecting garbage
Counts
4 → 1
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(*.f64 (-.f64 a b) (+.f64 b a))
Calls

5 calls:

4.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
2.0ms
b
2.0ms
a
2.0ms
(*.f64 b b)
1.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
100.0%1(*.f64 b b)
100.0%1(*.f64 a a)
100.0%1(-.f64 (*.f64 a a) (*.f64 b b))
100.0%1a
100.0%1b
Compiler

Compiled 15 to 15 computations (0% saved)

regimes6.0ms (0.3%)

Memory
16.8MiB live, 16.8MiB allocated; 0ms collecting garbage
Counts
2 → 2
Calls
Call 1
Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Calls

5 calls:

1.0ms
a
1.0ms
b
1.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
1.0ms
(*.f64 b b)
1.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
75.2%2(*.f64 b b)
82.8%2(*.f64 a a)
96.5%2(-.f64 (*.f64 a a) (*.f64 b b))
82.8%2a
75.2%2b
Compiler

Compiled 15 to 15 computations (0% saved)

regimes5.0ms (0.2%)

Memory
16.8MiB live, 16.8MiB allocated; 0ms collecting garbage
Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

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

5 calls:

1.0ms
a
1.0ms
b
1.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
1.0ms
(*.f64 a a)
1.0ms
(*.f64 b b)
Results
AccuracySegmentsBranch
59.4%1(*.f64 b b)
59.4%1b
59.4%1(*.f64 a a)
59.4%1a
59.4%1(-.f64 (*.f64 a a) (*.f64 b b))
Compiler

Compiled 15 to 15 computations (0% saved)

bsearch7.0ms (0.3%)

Memory
-53.8MiB live, 1.3MiB allocated; 10ms collecting garbage
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-1.5e-323
0.0
Compiler

Compiled 10 to 10 computations (0% saved)

simplify60.0ms (2.9%)

Memory
9.6MiB live, 56.7MiB allocated; 3ms collecting garbage
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01851
13951
210451
324751
442551
586051
6140951
7209351
8292451
9323451
10329651
11329651
12337451
Stop Event
1×saturated
Calls
Call 1
Inputs
(*.f64 (-.f64 a b) (+.f64 b a))
(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -1/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Outputs
(*.f64 (-.f64 a b) (+.f64 b a))
(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -1/101201126653655309176247673359458653524778324882071059178450679013715169783997673445980191850718562247593538932158405955694904368692896738433506699970369254960758712138283180682233453871046608170619883839236372534281003741712346349309051677824579778170405028256179384776166707307615251266093163754323003131653853870546747392 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))
#s(approx (- (* a a) (* b b)) (*.f64 a a))

derivations85.0ms (4.1%)

Memory
-4.1MiB live, 89.1MiB allocated; 6ms collecting garbage
Stop Event
1×done
Compiler

Compiled 51 to 18 computations (64.7% saved)

preprocess25.0ms (1.2%)

Memory
2.5MiB live, 51.9MiB allocated; 7ms collecting garbage
Remove

(abs a)

(abs b)

Compiler

Compiled 158 to 76 computations (51.9% saved)

end0.0ms (0%)

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

Profiling

Loading profile data...