Difference of squares

Time bar (total: 7.3s)

start0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated

analyze0.0ms (0%)

Memory
0.5MiB live, 0.5MiB allocated
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)

sample1.1s (14.8%)

Memory
18.7MiB live, 607.7MiB allocated
Samples
769.0ms8 256×0valid
Precisions
Click to see histograms. Total time spent on operations: 544.0ms
ival-mult: 444.0ms (81.7% of total)
ival-sub: 90.0ms (16.6% of total)
ival-true: 6.0ms (1.1% of total)
ival-assert: 3.0ms (0.6% of total)
Bogosity

explain115.0ms (1.6%)

Memory
1.5MiB live, 47.2MiB allocated
FPErrors
Click to see full error table
Ground TruthOverpredictionsExampleUnderpredictionsExampleSubexpression
220-0-(-.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-rescue220
↳(*.f64 a a)overflow67
↳(*.f64 b b)overflow68
Confusion
Predicted +Predicted -
+220
-0234
Precision
1.0
Recall
1.0
Confusion?
Predicted +Predicted MaybePredicted -
+2200
-00234
Precision?
1.0
Recall?
1.0
Freqs
test
numberfreq
0234
122
Total Confusion?
Predicted +Predicted MaybePredicted -
+100
-000
Precision?
1.0
Recall?
1.0
Samples
22.0ms512×0valid
Compiler

Compiled 56 to 24 computations (57.1% saved)

Precisions
Click to see histograms. Total time spent on operations: 10.0ms
ival-mult: 7.0ms (69.4% of total)
ival-sub: 2.0ms (19.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

preprocess637.0ms (8.8%)

Memory
-6.9MiB live, 150.8MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01338
15135
214435
336635
489235
5122335
6175435
7234035
8415235
9472735
10484035
11495435
12503435
13503435
14641535
15739335
16787735
17789335
18789335
057
087
1167
2277
3537
41147
53157
65677
712387
824957
941247
1049977
1153667
1255967
1357107
1457107
1566707
1668307
1771507
1871507
1975507
2077107
2177907
2277907
2377907
0102687
Stop Event
1×iter limit
1×node limit
1×iter limit
1×node limit
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
Outputs
(-.f64 (*.f64 a a) (*.f64 b b))
(fma.f64 (neg.f64 b) b (*.f64 a a))
Symmetry

(abs b)

(abs a)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval0.0ms (0%)

Memory
0.1MiB live, 0.1MiB allocated
Compiler

Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory
0.4MiB live, 0.4MiB allocated
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶91.4%
(-.f64 (*.f64 a a) (*.f64 b b))
Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify431.0ms (5.9%)

Memory
15.7MiB live, 124.1MiB allocated
Algorithm
1×egg-herbie
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
11615
22715
35315
411415
531515
656715
7123815
8249515
9412415
10499715
11536615
12559615
13571015
14571015
15667015
16683015
17715015
18715015
19755015
20771015
21779015
22779015
23779015
01026815
Stop Event
1×iter limit
1×node limit
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))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(*.f64 a a)
a
(*.f64 b b)
b

localize102.0ms (1.4%)

Memory
-45.2MiB live, 19.9MiB allocated
Localize:

Found 3 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 b b)
accuracy0.0
(*.f64 a a)
accuracy4.890604358302059
(-.f64 (*.f64 a a) (*.f64 b b))
Samples
10.0ms256×0valid
Compiler

Compiled 32 to 12 computations (62.5% saved)

Precisions
Click to see histograms. Total time spent on operations: 5.0ms
ival-mult: 3.0ms (65.7% of total)
ival-sub: 1.0ms (21.9% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series3.0ms (0%)

Memory
1.7MiB live, 1.7MiB allocated
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))

simplify207.0ms (2.8%)

Memory
18.9MiB live, 54.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01738
13938
211338
346938
4168938
5283938
6499438
0839738
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))
(*.f64 (-.f64 a b) (+.f64 b 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)
(*.f64 b b)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))

rewrite290.0ms (4%)

Memory
30.5MiB live, 219.9MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0513
0813
13213
221613
3196713
0877813
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
3 → 252
Calls
Call 1
Inputs
(-.f64 (*.f64 a a) (*.f64 b b))
(*.f64 a a)
(*.f64 b b)
Outputs
(*.f64 (pow.f64 (/.f64 (fma.f64 b b (*.f64 a a)) (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 b b (*.f64 a a)) (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64)))) #s(literal -1 binary64)) (pow.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64))) #s(literal -1 binary64)))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 (*.f64 b a) #s(literal 2 binary64))))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 3 binary64)) (pow.f64 b #s(literal 6 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))))
(*.f64 (/.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 b #s(literal 4 binary64)))) (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (+.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64))) (pow.f64 a #s(literal 4 binary64))))
(*.f64 (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))
(*.f64 (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))))
(*.f64 #s(literal 1 binary64) (*.f64 (-.f64 a b) (+.f64 b a)))
(*.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (pow.f64 (neg.f64 (fma.f64 b b (*.f64 a a))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (pow.f64 (neg.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))) #s(literal -1 binary64)))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(*.f64 (fma.f64 b b (*.f64 a a)) (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (fma.f64 b b (*.f64 a a))))
(*.f64 (fma.f64 b b (*.f64 a a)) (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)))
(*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (/.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(*.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64))))
(*.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))
(pow.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (-.f64 (pow.f64 (fma.f64 a a #s(literal 0 binary64)) #s(literal 3 binary64)) (pow.f64 b #s(literal 6 binary64))) (fma.f64 (fma.f64 a a #s(literal 0 binary64)) (fma.f64 a a #s(literal 0 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 (fma.f64 a a #s(literal 0 binary64)) (*.f64 b b)))))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 b b) (*.f64 a a)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (fma.f64 (-.f64 (*.f64 b b) (*.f64 a a)) (-.f64 (*.f64 b b) (*.f64 a a)) (*.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) (*.f64 a a))))))
(/.f64 (+.f64 (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 3 binary64)) (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 3 binary64))) (fma.f64 (*.f64 b (-.f64 a b)) (*.f64 b (-.f64 a b)) (-.f64 (*.f64 (*.f64 a (-.f64 a b)) (*.f64 a (-.f64 a b))) (*.f64 (*.f64 b (-.f64 a b)) (*.f64 a (-.f64 a b))))))
(/.f64 (+.f64 (pow.f64 (*.f64 a (-.f64 a b)) #s(literal 3 binary64)) (pow.f64 (*.f64 b (-.f64 a b)) #s(literal 3 binary64))) (fma.f64 (*.f64 a (-.f64 a b)) (*.f64 a (-.f64 a b)) (-.f64 (*.f64 (*.f64 b (-.f64 a b)) (*.f64 b (-.f64 a b))) (*.f64 (*.f64 a (-.f64 a b)) (*.f64 b (-.f64 a b))))))
(/.f64 (+.f64 (pow.f64 (*.f64 a (+.f64 b a)) #s(literal 3 binary64)) (pow.f64 (*.f64 (neg.f64 b) (+.f64 b a)) #s(literal 3 binary64))) (fma.f64 (*.f64 a (+.f64 b a)) (*.f64 a (+.f64 b a)) (-.f64 (*.f64 (*.f64 (neg.f64 b) (+.f64 b a)) (*.f64 (neg.f64 b) (+.f64 b a))) (*.f64 (*.f64 a (+.f64 b a)) (*.f64 (neg.f64 b) (+.f64 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 (*.f64 (-.f64 a b) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (-.f64 a b) b) #s(literal 3 binary64))) (fma.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) a) (-.f64 (*.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) b)) (*.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) b)))))
(/.f64 (+.f64 (pow.f64 (*.f64 (+.f64 b a) a) #s(literal 3 binary64)) (pow.f64 (*.f64 (+.f64 b a) (neg.f64 b)) #s(literal 3 binary64))) (fma.f64 (*.f64 (+.f64 b a) a) (*.f64 (+.f64 b a) a) (-.f64 (*.f64 (*.f64 (+.f64 b a) (neg.f64 b)) (*.f64 (+.f64 b a) (neg.f64 b))) (*.f64 (*.f64 (+.f64 b a) a) (*.f64 (+.f64 b a) (neg.f64 b))))))
(/.f64 (+.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 3 binary64))) (pow.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) #s(literal 2 binary64)) (-.f64 (*.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))) (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))) (*.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (neg.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))))))))
(/.f64 (+.f64 (pow.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)))) #s(literal 3 binary64)) (pow.f64 (neg.f64 (/.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))))) #s(literal 3 binary64))) (+.f64 (pow.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)))) #s(literal 2 binary64)) (-.f64 (*.f64 (neg.f64 (/.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))))) (neg.f64 (/.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 (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)))) (neg.f64 (/.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 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) #s(literal 1 binary64))) (neg.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 b a))) (neg.f64 (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (neg.f64 (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (+.f64 b a))) (neg.f64 (+.f64 b a)))
(/.f64 (neg.f64 (*.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b))) (neg.f64 (fma.f64 b (-.f64 b a) (*.f64 a a))))
(/.f64 (neg.f64 (*.f64 (*.f64 (-.f64 a b) (+.f64 b a)) (-.f64 a b))) (neg.f64 (-.f64 a b)))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal -1 binary64)))) (neg.f64 (+.f64 (+.f64 (pow.f64 (*.f64 b a) #s(literal 4 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 a #s(literal 8 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))) (neg.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 b b (*.f64 a a)) (*.f64 b b) (pow.f64 a #s(literal 4 binary64))) #s(literal -1 binary64)))) (neg.f64 (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))))
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(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 b #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 b #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (neg.f64 (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))) (/.f64 (/.f64 (pow.f64 b #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))) (/.f64 (/.f64 (pow.f64 b #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b a) #s(literal 6 binary64)))) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (*.f64 (fma.f64 b (-.f64 b a) (*.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a)))))
(-.f64 (/.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (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 (pow.f64 b #s(literal 12 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (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 (/.f64 (pow.f64 a #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b 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 (/.f64 (pow.f64 b #s(literal 18 binary64)) (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (*.f64 b 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 (fma.f64 a a #s(literal 0 binary64)) (*.f64 b b))
(-.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) (*.f64 a a)))
(-.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 a a) (*.f64 b b))
(exp.f64 (*.f64 (log.f64 (pow.f64 (*.f64 (-.f64 a b) (+.f64 b a)) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (*.f64 b (-.f64 a b)) (*.f64 a (-.f64 a b)))
(+.f64 (*.f64 a (-.f64 a b)) (*.f64 b (-.f64 a b)))
(+.f64 (*.f64 a (+.f64 b a)) (*.f64 (neg.f64 b) (+.f64 b a)))
(+.f64 (*.f64 (-.f64 a b) b) (*.f64 (-.f64 a b) a))
(+.f64 (*.f64 (-.f64 a b) a) (*.f64 (-.f64 a b) b))
(+.f64 (*.f64 (+.f64 b a) a) (*.f64 (+.f64 b a) (neg.f64 b)))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a))) (neg.f64 (/.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)))) (neg.f64 (/.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 a a))
(+.f64 (*.f64 a a) (*.f64 (neg.f64 b) b))
(*.f64 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(*.f64 (neg.f64 b) (neg.f64 b))
(*.f64 b b)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 b))
(pow.f64 (neg.f64 b) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))

eval1.7s (23.6%)

Memory
-38.8MiB live, 46.6MiB allocated
Compiler

Compiled 8 269 to 758 computations (90.8% saved)

prune4.0ms (0.1%)

Memory
19.2MiB live, 19.2MiB allocated
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New2542256
Fresh000
Picked101
Done000
Total2552257
Accuracy
100.0%
Counts
257 → 2
Alt Table
Click to see full alt table
StatusAccuracyProgram
▶100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
▶54.5%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify977.0ms (13.4%)

Memory
13.5MiB live, 241.7MiB allocated
Algorithm
1×egg-herbie
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
13434
25934
313934
428134
558434
6147334
7287034
8396634
9453334
10477234
11490234
12492434
13492434
14492434
0865834
Stop Event
1×iter limit
1×node limit
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)

localize26.0ms (0.4%)

Memory
12.3MiB live, 50.6MiB allocated
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)
accuracy29.088821113372276
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
Samples
20.0ms256×0valid
Compiler

Compiled 65 to 23 computations (64.6% saved)

Precisions
Click to see histograms. Total time spent on operations: 11.0ms
ival-mult: 6.0ms (52.5% of total)
ival-sub: 2.0ms (17.5% of total)
ival-add: 1.0ms (8.8% of total)
ival-neg: 1.0ms (8.8% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series61.0ms (0.8%)

Memory
-27.6MiB live, 64.6MiB allocated
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
56.0ms
b
@0
((- (* 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
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))

simplify118.0ms (1.6%)

Memory
8.4MiB live, 163.4MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092132
1281132
2837132
33582132
08444132
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)))))
(fma.f64 (neg.f64 b) b (*.f64 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)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
a
(* a (+ 1 (* -1 (/ b a))))
(-.f64 a b)
(* a (+ 1 (/ b a)))
(+.f64 b a)
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 (* a (- (/ b a) 1)))
(-.f64 a b)
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+.f64 b 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))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* (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))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* b (- (/ a b) 1))
(-.f64 a b)
(* b (+ 1 (/ a b)))
(+.f64 b a)
(* (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))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(-.f64 a b)
(* -1 (* b (- (* -1 (/ a b)) 1)))
(+.f64 b a)

rewrite128.0ms (1.8%)

Memory
16.8MiB live, 176.5MiB allocated
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01131
01631
16731
250431
3674924
0927824
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
6 → 723
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 b b))
(*.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)))
(*.f64 #s(literal 1 binary64) (*.f64 b b))
(*.f64 #s(literal -1 binary64) (*.f64 b b))
(*.f64 (*.f64 b b) #s(literal 1 binary64))
(*.f64 (*.f64 b b) #s(literal -1 binary64))
(*.f64 b b)
(pow.f64 (exp.f64 (log.f64 b)) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(/.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal 0 binary64)) (-.f64 (*.f64 b b) #s(literal 0 binary64)))
(/.f64 (+.f64 #s(literal 0 binary64) (pow.f64 b #s(literal 6 binary64))) (+.f64 #s(literal 0 binary64) (-.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (+.f64 (pow.f64 b #s(literal 6 binary64)) #s(literal 0 binary64)) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 (*.f64 b b) #s(literal 0 binary64)))))
(/.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 b b))
(/.f64 (pow.f64 b #s(literal 6 binary64)) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 b #s(literal 4 binary64)) (*.f64 #s(literal 0 binary64) (*.f64 b b)))))
(/.f64 (pow.f64 b #s(literal 3 binary64)) b)
(neg.f64 (*.f64 b b))
(fma.f64 (exp.f64 (log.f64 b)) (exp.f64 (log.f64 b)) #s(literal 0 binary64))
(fma.f64 #s(literal 1 binary64) (*.f64 b b) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 b b) #s(literal 0 binary64))
(fma.f64 (*.f64 b b) #s(literal 1 binary64) #s(literal 0 binary64))
(fma.f64 (*.f64 b b) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 b b #s(literal 0 binary64))
(-.f64 #s(literal 0 binary64) (*.f64 b b))
(exp.f64 (*.f64 (*.f64 (log.f64 b) #s(literal 1 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 (log.f64 b))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
(+.f64 #s(literal 0 binary64) (*.f64 b b))
(+.f64 (*.f64 b b) #s(literal 0 binary64))
(*.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)))
(*.f64 #s(literal -1 binary64) b)
(*.f64 (pow.f64 b #s(literal 3 binary64)) (pow.f64 (*.f64 b b) #s(literal -1 binary64)))
(*.f64 (*.f64 b b) (pow.f64 b #s(literal -1 binary64)))
(*.f64 b (/.f64 b b))
(*.f64 b #s(literal -1 binary64))
(pow.f64 (pow.f64 b #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 (*.f64 b b) (pow.f64 b #s(literal 3 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 b (*.f64 b b)) #s(literal -1 binary64))
(pow.f64 b #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 b b) (pow.f64 b #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 b (*.f64 b b)))
(/.f64 (pow.f64 b #s(literal 3 binary64)) (+.f64 #s(literal 0 binary64) (-.f64 (*.f64 b b) #s(literal 0 binary64))))
(/.f64 (pow.f64 b #s(literal 3 binary64)) (*.f64 b b))
(/.f64 (*.f64 b b) b)
(neg.f64 b)
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(+.f64 (*.f64 (/.f64 (-.f64 a b) (-.f64 b a)) b) (*.f64 (/.f64 (-.f64 a b) (-.f64 b a)) (neg.f64 a)))
(+.f64 (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (-.f64 a b) a)) (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 b b)))
(+.f64 (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 b b)) (*.f64 (/.f64 (pow.f64 (-.f64 b a) #s(literal 2 binary64)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (*.f64 (-.f64 a b) a)))
(+.f64 (-.f64 a #s(literal 0 binary64)) b)
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 a b) b (*.f64 a a))) (neg.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 b b (*.f64 (-.f64 b a) a)))))
(+.f64 (*.f64 b (/.f64 b (-.f64 b a))) (neg.f64 (*.f64 a (/.f64 a (-.f64 b a)))))
(+.f64 (*.f64 a (/.f64 a (-.f64 a b))) (neg.f64 (*.f64 b (/.f64 b (-.f64 b a)))))
(+.f64 #s(literal 0 binary64) (-.f64 a b))
(+.f64 b (neg.f64 (neg.f64 a)))
(+.f64 b a)
(+.f64 a (*.f64 #s(literal 1 binary64) b))
(+.f64 a b)

eval56.0ms (0.8%)

Memory
-5.6MiB live, 113.7MiB allocated
Compiler

Compiled 12 091 to 1 341 computations (88.9% saved)

prune10.0ms (0.1%)

Memory
-6.6MiB live, 31.3MiB allocated
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New5321533
Fresh000
Picked022
Done000
Total5323535
Accuracy
100.0%
Counts
535 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
✓54.5%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
▶52.9%
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify351.0ms (4.8%)

Memory
15.5MiB live, 252.4MiB allocated
Algorithm
1×egg-herbie
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
11615
22715
35315
411515
531815
658015
7125715
8253115
9417015
10503715
11540615
12563615
13575015
14575015
15671015
16687015
17719015
18719015
19759015
20775015
21783015
22783015
23783015
01039715
Stop Event
1×iter limit
1×node limit
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

localize31.0ms (0.4%)

Memory
-26.2MiB live, 23.4MiB allocated
Localize:

Found 2 expressions of interest:

NewMetricScoreProgram
accuracy0.0
(*.f64 a a)
accuracy30.141524404796186
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Samples
27.0ms256×0valid
Compiler

Compiled 28 to 14 computations (50% saved)

Precisions
Click to see histograms. Total time spent on operations: 21.0ms
ival-mult: 20.0ms (93.3% of total)
ival-sub: 1.0ms (4.7% of total)
ival-true: 0.0ms (0% of total)
ival-assert: 0.0ms (0% of total)

series2.0ms (0%)

Memory
3.5MiB live, 3.5MiB allocated
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))

simplify123.0ms (1.7%)

Memory
-3.3MiB live, 191.2MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01735
13935
211335
346935
4168935
5283935
6499435
0839735
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))
(*.f64 (-.f64 a b) (+.f64 b 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) (- (/ (pow a 2) (pow b 2)) 1))
(*.f64 (-.f64 a b) (+.f64 b a))

rewrite160.0ms (2.2%)

Memory
10.5MiB live, 239.5MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0714
0814
13214
221614
3196914
0878014
Stop Event
1×iter limit
1×node limit
1×iter limit
Counts
2 → 7
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 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(exp.f64 (*.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))

eval1.0ms (0%)

Memory
4.3MiB live, 4.3MiB allocated
Compiler

Compiled 129 to 32 computations (75.2% saved)

prune2.0ms (0%)

Memory
5.3MiB live, 5.3MiB allocated
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New10010
Fresh000
Picked011
Done022
Total10313
Accuracy
100.0%
Counts
13 → 3
Alt Table
Click to see full alt table
StatusAccuracyProgram
✓100.0%
(*.f64 (-.f64 a b) (+.f64 b a))
✓54.5%
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
✓52.9%
#s(approx (- (* a a) (* b b)) (*.f64 a a))
Compiler

Compiled 67 to 35 computations (47.8% saved)

regimes66.0ms (0.9%)

Memory
-28.6MiB live, 64.9MiB allocated
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:

58.0ms
b
2.0ms
a
2.0ms
(*.f64 b b)
2.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
2.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
100.0%1a
100.0%1b
100.0%1(-.f64 (*.f64 a a) (*.f64 b b))
100.0%1(*.f64 a a)
100.0%1(*.f64 b b)
Compiler

Compiled 15 to 15 computations (0% saved)

regimes7.0ms (0.1%)

Memory
18.6MiB live, 18.6MiB allocated
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 b b)
1.0ms
(-.f64 (*.f64 a a) (*.f64 b b))
1.0ms
(*.f64 a a)
Results
AccuracySegmentsBranch
77.3%2a
79.1%2b
95.5%2(-.f64 (*.f64 a a) (*.f64 b b))
77.3%2(*.f64 a a)
79.1%2(*.f64 b b)
Compiler

Compiled 15 to 15 computations (0% saved)

regimes7.0ms (0.1%)

Memory
-22.7MiB live, 15.8MiB allocated
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:

3.0ms
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
52.9%1a
52.9%1(*.f64 a a)
52.9%1b
52.9%1(*.f64 b b)
52.9%1(-.f64 (*.f64 a a) (*.f64 b b))
Compiler

Compiled 15 to 15 computations (0% saved)

bsearch0.0ms (0%)

Memory
0.9MiB live, 0.9MiB allocated
Algorithm
1×left-value
Steps
TimeLeftRight
0.0ms
-2.040928945177695e-281
0.0
Compiler

Compiled 10 to 10 computations (0% saved)

simplify25.0ms (0.4%)

Memory
20.6MiB live, 58.7MiB allocated
Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01851
12951
23551
33851
43951
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 -3269984763141685/163499238157084246970890052651977815332245607254872681799888670100456398181905536269103756533156716633238933245476249210386222120009203192687752953715493389952614864728152938620316690140722215910002962984513038253533659992483501702257775023591263777382983344691261934931342007929269781293292322816 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))
(*.f64 (+.f64 b a) (-.f64 a b))
(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -3269984763141685/163499238157084246970890052651977815332245607254872681799888670100456398181905536269103756533156716633238933245476249210386222120009203192687752953715493389952614864728152938620316690140722215910002962984513038253533659992483501702257775023591263777382983344691261934931342007929269781293292322816 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))

soundness473.0ms (6.5%)

Memory
-21.0MiB live, 381.4MiB allocated
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
092132
1281132
2837132
33582132
08444132
01738
13938
211338
346938
4168938
5283938
6499438
0839738
0513
0813
13213
221613
3196713
0877813
Stop Event
1×done
1×iter limit
1×node limit
1×iter limit
1×iter limit
1×node limit
1×iter limit
1×node limit
Compiler

Compiled 83 to 44 computations (47% saved)

preprocess67.0ms (0.9%)

Memory
7.3MiB live, 46.1MiB allocated
Remove

(abs a)

(abs b)

Compiler

Compiled 186 to 96 computations (48.4% saved)

end0.0ms (0%)

Memory
0.0MiB live, 0.0MiB allocated

Profiling

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