Details

Time bar (total: 3.8s)

analyze220.0ms (5.7%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%68.7%6.3%6
25%56.2%18.8%7
25%48.4%26.6%8
25%35.1%39.9%9
28.1%18.3%53.6%10
31.6%12.3%56.1%11
33.4%5.9%60.8%12
35.2%3.8%61%13
36.1%2.9%61%14
Compiler

Compiled 34 to 22 computations (35.3% saved)

sample32.0ms (0.8%)

Algorithm
intervals
Results
24.0ms256×body128valid
Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify64.0ms (1.7%)

Algorithm
egg-herbie
Rules
725×fma-def_binary64
669×unsub-neg_binary64
596×cancel-sign-sub-inv_binary64
340×+-commutative_binary64
277×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
02042
16340
217036
354236
4186732
5328132
6488132
7495832

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.0b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.2b
(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)
0.0b
(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 172 to 108 computations (37.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a -3 1)
0.1b
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.1b
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
1.0b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite8.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-sqr-sqrt_binary64
fma-udef_binary64
Counts
4 → 53
Calls

4 calls:

5.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
0.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
0.0ms
(fma.f64 a -3 1)

series116.0ms (3%)

Counts
4 → 84
Calls

4 calls:

50.0ms
(fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
32.0ms
(*.f64 (*.f64 b b) (fma.f64 a -3 1))
28.0ms
(fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1)))
5.0ms
(fma.f64 a -3 1)

simplify125.0ms (3.3%)

Algorithm
egg-herbie
Rules
786×fma-def_binary64
528×fma-neg_binary64
415×associate-+l+_binary64
313×cancel-sign-sub-inv_binary64
229×associate-+r+_binary64
Counts
137 → 250
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01252754
13182352
29692192
331842169
448182143
549832143

prune164.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New2464250
Fresh101
Picked101
Done000
Total2484252
Error
0.0b
Counts
252 → 4
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4)) -1)
15.1b
(+.f64 (cbrt.f64 (*.f64 (*.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)))) -1)
0.0b
(+.f64 (fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
9.3b
(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -1)
Compiler

Compiled 3780 to 2134 computations (43.5% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 a a (pow.f64 a 3))
0.0b
(fma.f64 a -3 1)
0.1b
(fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
1.0b
(*.f64 (*.f64 b b) (fma.f64 a -3 1))

rewrite2.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 20
Calls

2 calls:

0.0ms
(fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms
(fma.f64 a a (pow.f64 a 3))

series57.0ms (1.5%)

Counts
2 → 36
Calls

2 calls:

42.0ms
(fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
14.0ms
(fma.f64 a a (pow.f64 a 3))

simplify91.0ms (2.4%)

Algorithm
egg-herbie
Rules
648×fma-neg_binary64
620×fma-def_binary64
488×cancel-sign-sub-inv_binary64
474×distribute-rgt-in_binary64
416×associate-+l+_binary64
Counts
56 → 96
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0741427
11971274
26061124
325111101
449551075
552841075

prune181.0ms (4.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New2191220
Fresh123
Picked011
Done000
Total2204224
Error
0.0b
Counts
224 → 4
Alt Table
StatusErrorProgram
0.1b
(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4)) -1)
15.1b
(+.f64 (cbrt.f64 (pow.f64 (fma.f64 4 (fma.f64 (*.f64 b b) (fma.f64 a -3 1) (fma.f64 a a (pow.f64 a 3))) (pow.f64 (hypot.f64 a b) 4)) 3)) -1)
0.0b
(+.f64 (fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
9.3b
(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -1)
Compiler

Compiled 3369 to 2139 computations (36.5% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))
0.0b
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
0.0b
(*.f64 a (fma.f64 a 2 -12))
1.4b
(*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))

rewrite19.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
10×*-un-lft-identity_binary64
Counts
4 → 75
Calls

4 calls:

9.0ms
(*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
4.0ms
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
3.0ms
(*.f64 a (fma.f64 a 2 -12))
0.0ms
(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))

series115.0ms (3%)

Counts
4 → 84
Calls

4 calls:

39.0ms
(*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))
37.0ms
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12))))) (pow.f64 a 4))
30.0ms
(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (+.f64 (fma.f64 b b 4) (*.f64 a (fma.f64 a 2 -12)))))
9.0ms
(*.f64 a (fma.f64 a 2 -12))

simplify130.0ms (3.4%)

Algorithm
egg-herbie
Rules
662×fma-neg_binary64
633×associate-+l+_binary64
400×*-commutative_binary64
389×associate-+r+_binary64
354×exp-sum_binary64
Counts
159 → 293
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01764633
14903460
217243385
337823385
450683385

prune251.0ms (6.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2921293
Fresh112
Picked101
Done011
Total2943297
Error
0.0b
Counts
297 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4)) -1)
9.3b
(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -1)
0.0b
(+.f64 (fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 6484 to 4269 computations (34.2% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))))
0.0b
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4))
0.1b
(*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
0.1b
(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))

rewrite17.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
Counts
4 → 74
Calls

4 calls:

4.0ms
(*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
3.0ms
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4))
3.0ms
(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))
0.0ms
(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))))

series153.0ms (4%)

Counts
4 → 96
Calls

4 calls:

41.0ms
(*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))
39.0ms
(fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))))
37.0ms
(+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4))
34.0ms
(*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4)))

simplify145.0ms (3.8%)

Algorithm
egg-herbie
Rules
526×associate-+l+_binary64
457×distribute-rgt-in_binary64
441×fma-neg_binary64
440×distribute-lft-in_binary64
260×cancel-sign-sub-inv_binary64
Counts
170 → 293
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01695201
14464521
214213742
347433742
450703742

prune200.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New2930293
Fresh011
Picked011
Done011
Total2933296
Error
0.0b
Counts
296 → 3
Alt Table
StatusErrorProgram
0.0b
(+.f64 (+.f64 (fma.f64 4 (fma.f64 a a (pow.f64 a 3)) (*.f64 b (*.f64 b (fma.f64 a (fma.f64 2 a -12) (fma.f64 b b 4))))) (pow.f64 a 4)) -1)
9.3b
(+.f64 (+.f64 (*.f64 4 (pow.f64 a 2)) (+.f64 (*.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (*.f64 2 (*.f64 (pow.f64 a 2) (pow.f64 b 2)))))) -1)
0.0b
(+.f64 (fma.f64 4 (+.f64 (fma.f64 a a (pow.f64 a 3)) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)
Compiler

Compiled 5447 to 3618 computations (33.6% saved)

regimes598.0ms (15.5%)

Accuracy

Total 0.0b remaining (45%)

Threshold costs 0.0b (45%)

Compiler

Compiled 13051 to 9020 computations (30.9% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
+-commutative_binary64
*-commutative_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01834
12334
22234

end1.0ms (0%)

Compiler

Compiled 26 to 18 computations (30.8% saved)

sample1.1s (28.4%)

Algorithm
intervals
Results
737.0ms8000×body128valid
0.0msbody128invalid
Compiler

Compiled 147 to 104 computations (29.3% saved)

Profiling

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