Details

Time bar (total: 5.6s)

analyze859.0ms (15.2%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
6.2%93.6%0.2%9
6.2%82.7%11.1%10
12.5%73.7%13.8%11
15.6%59.5%25%12
17.9%53.3%28.8%13
22.4%47.2%30.4%14
Compiler

Compiled 18 to 12 computations (33.3% saved)

sample239.0ms (4.2%)

Algorithm
intervals
Results
14.0ms256×body128valid
4.0ms84×body128invalid
Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify63.0ms (1.1%)

Algorithm
egg-herbie
Rules
853×fma-neg_binary64
525×fma-def_binary64
182×cancel-sign-sub-inv_binary64
160×associate-*l*_binary64
154×distribute-rgt-in_binary64
Counts
1 → 2
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01219
12517
27217
322717
451217
5104417
6143617
7149217
8157317
9161517
10163117
11163117
12155017

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
5.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
5.3b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
Compiler

Compiled 61 to 35 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(-.f64 t (*.f64 z z))
4.9b
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

series37.0ms (0.7%)

Counts
2 → 72
Calls

2 calls:

32.0ms
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))
5.0ms
(-.f64 t (*.f64 z z))

rewrite4.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-log-exp_binary64
fma-neg_binary64
Counts
2 → 31
Calls

2 calls:

2.0ms
(-.f64 t (*.f64 z z))
0.0ms
(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

simplify277.0ms (4.9%)

Algorithm
egg-herbie
Rules
703×distribute-rgt-in_binary64
653×distribute-lft-in_binary64
495×fma-neg_binary64
369×exp-prod_binary64
193×fma-def_binary64
Counts
103 → 64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0801591
11871301
24311282
315351282
445881282
550851282

prune77.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New58664
Fresh000
Picked101
Done000
Total59665
Error
4.7b
Counts
65 → 6
Alt Table
StatusErrorProgram
15.5b
(fma.f64 x x (*.f64 4 (*.f64 y t)))
39.8b
(pow.f64 x 2)
36.6b
(*.f64 4 (*.f64 y t))
21.0b
(fma.f64 y (*.f64 4 (/.f64 (-.f64 (*.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
6.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
5.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
Compiler

Compiled 1269 to 517 computations (59.3% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
0.0b
(*.f64 4 (*.f64 y (pow.f64 z 2)))
0.0b
(*.f64 4 (*.f64 y t))
10.5b
(*.f64 y (pow.f64 z 2))

series58.0ms (1%)

Counts
4 → 12
Calls

4 calls:

34.0ms
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
10.0ms
(*.f64 4 (*.f64 y (pow.f64 z 2)))
8.0ms
(*.f64 y (pow.f64 z 2))
6.0ms
(*.f64 4 (*.f64 y t))

rewrite27.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
24×add-exp-log_binary64
17×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
13×prod-exp_binary64
11×*-un-lft-identity_binary64
Counts
4 → 92
Calls

4 calls:

7.0ms
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
7.0ms
(*.f64 4 (*.f64 y t))
4.0ms
(*.f64 4 (*.f64 y (pow.f64 z 2)))
4.0ms
(*.f64 y (pow.f64 z 2))

simplify86.0ms (1.5%)

Algorithm
egg-herbie
Rules
475×fma-def_binary64
426×*-commutative_binary64
396×cancel-sign-sub-inv_binary64
345×fma-neg_binary64
265×exp-prod_binary64
Counts
104 → 153
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01571684
13591327
212311244
332001237
446471237
548161237

prune155.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1503153
Fresh325
Picked011
Done000
Total1536159
Error
0.0b
Counts
159 → 6
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))
5.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
29.1b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 z y) (pow.f64 (sqrt.f64 z) 2))))
21.0b
(fma.f64 y (*.f64 4 (/.f64 (-.f64 (*.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
6.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
5.3b
(+.f64 (fma.f64 x x (*.f64 4 (*.f64 y (-.f64 t (*.f64 z z))))) 0)
Compiler

Compiled 3742 to 2314 computations (38.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))
0.0b
(*.f64 4 (*.f64 (*.f64 y z) z))
0.0b
(*.f64 4 (*.f64 y t))
0.2b
(*.f64 (*.f64 y z) z)

series57.0ms (1%)

Counts
3 → 96
Calls

3 calls:

38.0ms
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))
11.0ms
(*.f64 4 (*.f64 (*.f64 y z) z))
8.0ms
(*.f64 (*.f64 y z) z)

rewrite20.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
17×add-cbrt-cube_binary64
17×add-exp-log_binary64
17×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
3 → 65
Calls

3 calls:

9.0ms
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))
5.0ms
(*.f64 4 (*.f64 (*.f64 y z) z))
4.0ms
(*.f64 (*.f64 y z) z)

simplify109.0ms (1.9%)

Algorithm
egg-herbie
Rules
597×distribute-rgt-neg-in_binary64
513×fma-def_binary64
394×*-commutative_binary64
383×fma-neg_binary64
208×cancel-sign-sub-inv_binary64
Counts
161 → 113
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01262543
13122198
211662045
332792036
449992036
548692036

prune156.0ms (2.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1374141
Fresh224
Picked011
Done011
Total1398147
Error
0.0b
Counts
147 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))
5.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
0.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))))
21.7b
(*.f64 (sqrt.f64 (-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))) (sqrt.f64 (-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))))
0.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y z) z)) (cbrt.f64 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 (*.f64 y z) z)))))
5.3b
(fma.f64 x x (*.f64 y (*.f64 4 (-.f64 t (*.f64 z z)))))
21.0b
(fma.f64 y (*.f64 4 (/.f64 (-.f64 (*.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
6.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
Compiler

Compiled 3619 to 1866 computations (48.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 y z) z)
0.2b
(*.f64 (*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))))
0.4b
(*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))))
24.8b
(cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))

series1.1s (19%)

Counts
3 → 72
Calls

3 calls:

566.0ms
(*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))))
454.0ms
(cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))
49.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))))

rewrite59.0ms (1%)

Algorithm
rewrite-expression-head
Rules
29×pow1_binary64
16×pow1/3_binary64
11×pow-prod-up_binary64
11×add-sqr-sqrt_binary64
10×add-exp-log_binary64
Counts
3 → 79
Calls

3 calls:

46.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))))
5.0ms
(*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))))
4.0ms
(cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))

simplify109.0ms (1.9%)

Algorithm
egg-herbie
Rules
763×fma-neg_binary64
362×fma-def_binary64
313×unswap-sqr_binary64
259×*-commutative_binary64
207×exp-prod_binary64
Counts
151 → 128
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01502850
13052567
27692211
316562034
447282034
552952034

prune393.0ms (7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New2690269
Fresh055
Picked011
Done022
Total2698277
Error
0.0b
Counts
277 → 8
Alt Table
StatusErrorProgram
0.1b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))
5.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 y (pow.f64 z 2))))
0.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 (*.f64 (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))) (cbrt.f64 (*.f64 4 (*.f64 (*.f64 y z) z)))))
21.7b
(*.f64 (sqrt.f64 (-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))) (sqrt.f64 (-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 y z) z)))))
0.3b
(-.f64 (+.f64 (*.f64 4 (*.f64 y t)) (pow.f64 x 2)) (*.f64 4 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 y z) z)) (cbrt.f64 (*.f64 (*.f64 y z) z))) (cbrt.f64 (*.f64 (*.f64 y z) z)))))
5.3b
(fma.f64 x x (*.f64 y (*.f64 4 (-.f64 t (*.f64 z z)))))
21.0b
(fma.f64 y (*.f64 4 (/.f64 (-.f64 (*.f64 t t) (pow.f64 z 4)) (fma.f64 z z t))) (*.f64 x x))
6.5b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x)))) (cbrt.f64 (fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))))
Compiler

Compiled 10936 to 5482 computations (49.9% saved)

regimes654.0ms (11.6%)

Accuracy

Total 0.1b remaining (71.2%)

Threshold costs 0.1b (71.2%)

Counts
59 → 1
Compiler

Compiled 14077 to 9638 computations (31.5% saved)

simplify4.0ms (0.1%)

Algorithm
egg-herbie
Rules
10×*-commutative_binary64
+-commutative_binary64
distribute-lft-neg-in_binary64
distribute-rgt-neg-in_binary64
sub-neg_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01525
12725
23525
34525
45725
56425
66825
76925
86825

end1.0ms (0%)

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample1.1s (18.7%)

Algorithm
intervals
Results
407.0ms8000×body128valid
143.0ms3024×body128invalid
Compiler

Compiled 286 to 175 computations (38.8% saved)

Profiling

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