Details

analyze219.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
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
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample59.0ms (0.9%)

Algorithm

1×

intervals

Results

25.0ms	59×	body	1024	valid
11.0ms	141×	body	128	valid
7.0ms	33×	body	512	valid
3.0ms	6×	body	2048	valid
3.0ms	17×	body	256	valid
0.0ms	6×	body	128	invalid
0.0ms	6×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify161.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5212	41

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

28.5b

Counts

2 → 2

Compiler

Compiled 83 to 71 computations (14.5% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 eps) x)
0.1b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.1b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite58.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_428`
74×	`exp-neg_binary64_466`
72×	`frac-times_binary64_429`
56×	`exp-diff_binary64_467` `neg-sub0_binary64_414`
38×	`associate-*l/_binary64_362`
36×	`associate-*r/_binary64_361`
28×	`flip3-+_binary64_422` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394`
18×	`un-div-inv_binary64_417`
12×	`exp-prod_binary64_471`
10×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
8×	`add-cube-cbrt_binary64_454`
6×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
4×	`associate-l_binary64_360` `rem-exp-log_binary64_459`
3×	`associate-r_binary64_359`
2×	`distribute-lft-neg-in_binary64_376` `neg-mul-1_binary64_415` `distribute-rgt-neg-in_binary64_377` `neg-log_binary64_512`
1×	`pow-prod-down_binary64_490` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `distribute-lft-out_binary64_370` `*-commutative_binary64_350` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 148

Calls

4 calls:

19.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
6.0ms	(*.f64 (+.f64 1 eps) x)
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series189.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
19.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
17.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
16.0ms	(*.f64 (+.f64 1 eps) x)

simplify169.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4984	8219
1	4984	8219

prune423.0ms (6.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Error

0.2b

Counts

162 → 3

Compiler

Compiled 7619 to 5890 computations (22.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
6.2b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
12×	`associate-l_binary64_360`
7×	`add-log-exp_binary64_458` `add-exp-log_binary64_457`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
4×	`unpow-prod-down_binary64_498` `unswap-sqr_binary64_387` `cube-prod_binary64_447` `add-cbrt-cube_binary64_455`
3×	`associate-r_binary64_359` `prod-exp_binary64_468`
2×	`sqr-pow_binary64_391` `diff-log_binary64_511` `pow1_binary64_480`
1×	`associate--l+_binary64_356` `sub-neg_binary64_412` `difference-of-squares_binary64_388` `unpow3_binary64_485` `cube-mult_binary64_449` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sum-log_binary64_510` `flip3--_binary64_423` `pow-to-exp_binary64_488` `*-commutative_binary64_350` `flip--_binary64_394` `cancel-sign-sub-inv_binary64_385`

Counts

2 → 46

Calls

2 calls:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 3) 2/3)

series42.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(*.f64 (pow.f64 x 3) 2/3)
19.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4879	687
1	4879	687

prune58.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	50	5	55

Error

0.2b

Counts

55 → 5

Compiler

Compiled 1109 to 826 computations (25.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
0.8b	(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2))) (-.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)) x))
4.9b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))
4.9b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_441`
18×	`*-un-lft-identity_binary64_419`
16×	`associate-l_binary64_360`
14×	`add-cube-cbrt_binary64_454`
11×	`add-exp-log_binary64_457`
9×	`associate-r_binary64_359`
8×	`add-cbrt-cube_binary64_455` `pow1_binary64_480`
7×	`sqrt-prod_binary64_435`
6×	`cancel-sign-sub-inv_binary64_385`
5×	`flip3-+_binary64_422` `unswap-sqr_binary64_387` `flip-+_binary64_393`
4×	`sqrt-div_binary64_436` `unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `distribute-rgt-in_binary64_369` `frac-times_binary64_429` `prod-exp_binary64_468` `distribute-lft-in_binary64_368` `cube-prod_binary64_447`
3×	`flip3--_binary64_423` `flip--_binary64_394`
2×	`associate-l/_binary64_362` `sub-neg_binary64_412` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `cbrt-unprod_binary64_452` `sqr-pow_binary64_391` `associate-r/_binary64_361` `*-commutative_binary64_350` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432`
1×	`pow-prod-down_binary64_490` `unpow3_binary64_485` `cube-mult_binary64_449` `pow-exp_binary64_487` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488`

Counts

4 → 99

Calls

4 calls:

20.0ms	(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2))) (-.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)) x))
6.0ms	(*.f64 (pow.f64 x 3) 2/3)
5.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))
5.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))

series126.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

61.0ms	(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2))) (-.f64 (sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)) x))
23.0ms	(*.f64 (pow.f64 x 3) 2/3)
21.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))
21.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4945	2447
1	4945	2447

prune192.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	111	5	116

Error

0.2b

Counts

116 → 5

Compiler

Compiled 3533 to 2876 computations (18.6% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (pow.f64 x 3) (sqrt.f64 2))
0.8b	(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2))) (-.f64 (-.f64 (+.f64 (sqrt.f64 2) (.f64 1/3 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (.f64 1/36 (/.f64 (pow.f64 x 6) (sqrt.f64 2)))) x))
4.9b	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))
10.5b	(-.f64 (+.f64 (sqrt.f64 2) (.f64 1/3 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (.f64 1/36 (/.f64 (pow.f64 x 6) (sqrt.f64 2))))

rewrite68.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`times-frac_binary64_425`
61×	`add-sqr-sqrt_binary64_441`
60×	`*-un-lft-identity_binary64_419`
56×	`add-cube-cbrt_binary64_454`
42×	`sqrt-prod_binary64_435`
21×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
12×	`associate-/l*_binary64_364`
11×	`add-exp-log_binary64_457`
9×	`associate--l+_binary64_356` `add-log-exp_binary64_458` `cancel-sign-sub-inv_binary64_385`
8×	`add-cbrt-cube_binary64_455`
7×	`distribute-rgt-in_binary64_369` `unpow3_binary64_485` `cube-mult_binary64_449` `sqr-pow_binary64_391` `distribute-lft-in_binary64_368` `pow1_binary64_480`
6×	`associate-/r*_binary64_363`
5×	`flip3-+_binary64_422` `sub-neg_binary64_412` `associate-r_binary64_359` `flip-+_binary64_393`
4×	`frac-times_binary64_429` `flip3--_binary64_423` `associate-r/_binary64_361` `associate-l*_binary64_360` `flip--_binary64_394`
3×	`div-exp_binary64_470`
2×	`associate-*l/_binary64_362` `sqrt-div_binary64_436` `diff-log_binary64_511` `frac-sub_binary64_428`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `difference-of-squares_binary64_388` `pow1/2_binary64_499` `div-inv_binary64_416` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `pow-to-exp_binary64_488` `*-commutative_binary64_350` `frac-2neg_binary64_430` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `cbrt-undiv_binary64_453`

Counts

4 → 178

Calls

4 calls:

22.0ms	(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2))) (-.f64 (-.f64 (+.f64 (sqrt.f64 2) (.f64 1/3 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (.f64 1/36 (/.f64 (pow.f64 x 6) (sqrt.f64 2)))) x))
10.0ms	(-.f64 (+.f64 (sqrt.f64 2) (.f64 1/3 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (.f64 1/36 (/.f64 (pow.f64 x 6) (sqrt.f64 2))))
8.0ms	(/.f64 (pow.f64 x 3) (sqrt.f64 2))
6.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))

series213.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(-.f64 (+.f64 (sqrt.f64 2) (.f64 1/3 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (.f64 1/36 (/.f64 (pow.f64 x 6) (sqrt.f64 2))))
66.0ms	(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2))) (-.f64 (-.f64 (+.f64 (sqrt.f64 2) (.f64 1/3 (/.f64 (pow.f64 x 3) (sqrt.f64 2)))) (.f64 1/36 (/.f64 (pow.f64 x 6) (sqrt.f64 2)))) x))
44.0ms	(/.f64 (pow.f64 x 3) (sqrt.f64 2))
20.0ms	(sqrt.f64 (+.f64 (*.f64 (pow.f64 x 3) 2/3) 2))

simplify110.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5033	6072

prune578.0ms (8.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	188	2	190
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	190	5	195

Error

0.2b

Counts

195 → 5

Compiler

Compiled 8619 to 7267 computations (15.7% saved)

regimes527.0ms (7.7%)

Accuracy

Total 0.5b remaining (56.4%)

Threshold costs 0.5b (56.4%)

Compiler

Compiled 7468 to 6300 computations (15.6% saved)

bsearch80.0ms (1.2%)

Steps

Iters	Range		Point
8	0.06632113850749799	527.7097319761815	448.5223692902876

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	152
1	69	152

end0.0ms (0%)

sample3.3s (48.3%)

Algorithm

1×

intervals

Results

791.0ms	1985×	body	1024	valid
328.0ms	4271×	body	128	valid
241.0ms	1012×	body	512	valid
147.0ms	225×	body	2048	valid
77.0ms	507×	body	256	valid
17.0ms	213×	body	128	invalid
13.0ms	183×	body	128	overflowed
7.0ms	19×	body	1024	invalid
1.0ms	5×	body	512	invalid
1.0ms	6×	body	256	invalid

Compiler

Compiled 1967 to 1656 computations (15.8% saved)

Details

analyze219.0ms (3.2%)

sample59.0ms (0.9%)

simplify161.0ms (2.3%)

prune5.0ms (0.1%)

localize20.0ms (0.3%)

rewrite58.0ms (0.8%)

series189.0ms (2.8%)

simplify169.0ms (2.5%)

prune423.0ms (6.2%)

localize8.0ms (0.1%)

rewrite18.0ms (0.3%)

series42.0ms (0.6%)

simplify61.0ms (0.9%)

prune58.0ms (0.8%)

localize11.0ms (0.2%)

rewrite47.0ms (0.7%)

series126.0ms (1.8%)

simplify70.0ms (1%)

prune192.0ms (2.8%)

localize20.0ms (0.3%)

rewrite68.0ms (1%)

series213.0ms (3.1%)

simplify110.0ms (1.6%)

prune578.0ms (8.5%)

regimes527.0ms (7.7%)

bsearch80.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.3s (48.3%)

Profiling