Details

analyze452.0ms (6.3%)

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
6.2%	93.6%	0.1%	6
12.5%	87.4%	0.1%	7
15.6%	84.3%	0.1%	8
18.7%	71.8%	9.5%	9
23.4%	56%	20.6%	10
26.3%	52.2%	21.5%	11
31%	40.1%	28.9%	12
35.6%	28.9%	35.5%	13
36.8%	27.5%	35.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample26.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
4.0ms	92×	body	128	nan

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	18
1	38	18

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

21.0b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

19.8b	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
0.0b	(*.f64 x (+.f64 y z))
0.0b	(*.f64 x (+.f64 y z))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
19.8b	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_19537`
8×	`*-un-lft-identity_binary64_19515`
6×	`add-cube-cbrt_binary64_19550` `pow1_binary64_19576`
5×	`add-log-exp_binary64_19554` `add-cbrt-cube_binary64_19551` `add-exp-log_binary64_19553`
4×	`associate-r_binary64_19455`
3×	`associate-l_binary64_19456` `flip-+_binary64_19489` `sqrt-prod_binary64_19531` `flip3-+_binary64_19518`
2×	`associate-*r/_binary64_19457` `distribute-rgt-in_binary64_19465` `associate-+l+_binary64_19448` `distribute-lft-in_binary64_19464` `sqrt-div_binary64_19532`
1×	`distribute-lft-out_binary64_19466` `cbrt-unprod_binary64_19548` `sqrt-pow1_binary64_19533` `pow1/2_binary64_19595` `*-commutative_binary64_19446` `prod-exp_binary64_19564` `pow-prod-down_binary64_19586` `rem-sqrt-square_binary64_19528` `unswap-sqr_binary64_19483` `+-commutative_binary64_19445` `sum-log_binary64_19606`

Counts

3 → 51

Calls

6 calls:

6.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
6.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
6.0ms	(*.f64 x (+.f64 y z))
0.0ms	(*.f64 x (+.f64 y z))
0.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))

series390.0ms (5.4%)

Counts

3 → 47

Calls

3 calls:

153.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
149.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
88.0ms	(*.f64 x (+.f64 y z))

Compiler

Compiled 1471 to 1171 computations (20.4% saved)

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5404	1350

prune136.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	82	16	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	16	99

Error

20.4b

Counts

99 → 16

Compiler

Compiled 1812 to 666 computations (63.2% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z))))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z))))
0.0b	(*.f64 x (+.f64 y z))
0.0b	(*.f64 x (+.f64 y z))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
19.8b	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
19.8b	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_19537` `add-log-exp_binary64_19554`
6×	`add-cube-cbrt_binary64_19550` `pow1_binary64_19576` `*-un-lft-identity_binary64_19515` `sqrt-prod_binary64_19531`
4×	`flip-+_binary64_19489` `add-cbrt-cube_binary64_19551` `associate-+l+_binary64_19448` `sqrt-div_binary64_19532` `flip3-+_binary64_19518` `add-exp-log_binary64_19553`
2×	`distribute-rgt-in_binary64_19465` `sqrt-pow1_binary64_19533` `pow1/2_binary64_19595` `distribute-lft-in_binary64_19464` `rem-sqrt-square_binary64_19528` `+-commutative_binary64_19445` `sum-log_binary64_19606`

Counts

4 → 56

Calls

8 calls:

7.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
7.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
7.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
6.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
0.0ms	(*.f64 x (+.f64 y z))

series624.0ms (8.6%)

Counts

4 → 64

Calls

4 calls:

165.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
159.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
153.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
146.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))

Compiler

Compiled 3642 to 2650 computations (27.2% saved)

simplify63.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5022	2090

prune135.0ms (1.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	1	14	15
Picked	1	0	1
Done	0	0	0
Total	120	16	136

Error

20.4b

Counts

136 → 16

Compiler

Compiled 3790 to 855 computations (77.4% saved)

localize18.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 y x) (.f64 z (+.f64 x y)))))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z))))
0.0b	(*.f64 z (+.f64 x y))
0.0b	(*.f64 x (+.f64 y z))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
1.6b	(+.f64 (.f64 y x) (.f64 z (+.f64 x y)))
19.8b	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
19.8b	(sqrt.f64 (+.f64 (.f64 y x) (.f64 z (+.f64 x y))))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_19537` `add-log-exp_binary64_19554`
6×	`add-cube-cbrt_binary64_19550` `pow1_binary64_19576` `*-un-lft-identity_binary64_19515` `sqrt-prod_binary64_19531`
4×	`flip-+_binary64_19489` `add-cbrt-cube_binary64_19551` `sqrt-div_binary64_19532` `flip3-+_binary64_19518` `add-exp-log_binary64_19553`
2×	`distribute-rgt-in_binary64_19465` `sqrt-pow1_binary64_19533` `pow1/2_binary64_19595` `associate-+l+_binary64_19448` `associate-+r+_binary64_19447` `distribute-lft-in_binary64_19464` `rem-sqrt-square_binary64_19528` `+-commutative_binary64_19445` `sum-log_binary64_19606`

Counts

4 → 56

Calls

8 calls:

9.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
6.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
4.0ms	(+.f64 (.f64 y x) (.f64 z (+.f64 x y)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y x) (.f64 z (+.f64 x y))))
0.0ms	(*.f64 x (+.f64 y z))

series642.0ms (8.9%)

Counts

4 → 64

Calls

4 calls:

168.0ms	(sqrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
162.0ms	(sqrt.f64 (+.f64 (.f64 y x) (.f64 z (+.f64 x y))))
162.0ms	(+.f64 (.f64 y x) (.f64 z (+.f64 x y)))
149.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))

Compiler

Compiled 3642 to 2646 computations (27.3% saved)

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5000	2090

prune126.0ms (1.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	120	16	136

Error

20.4b

Counts

136 → 16

Compiler

Compiled 3765 to 873 computations (76.8% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(.f64 (fabs.f64 (cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))) (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (*.f64 y z)))))
0.1b	(sqrt.f64 (cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z))))
0.0b	(*.f64 x (+.f64 y z))
0.0b	(*.f64 x (+.f64 y z))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
1.4b	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
20.4b	(cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
20.4b	(cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_19554`
6×	`add-cube-cbrt_binary64_19550` `add-sqr-sqrt_binary64_19537` `cbrt-prod_binary64_19546` `*-un-lft-identity_binary64_19515`
4×	`flip-+_binary64_19489` `pow1_binary64_19576` `add-cbrt-cube_binary64_19551` `associate-+l+_binary64_19448` `cbrt-div_binary64_19547` `flip3-+_binary64_19518` `add-exp-log_binary64_19553`
2×	`distribute-rgt-in_binary64_19465` `pow1/3_binary64_19597` `distribute-lft-in_binary64_19464` `+-commutative_binary64_19445` `sum-log_binary64_19606`

Counts

4 → 52

Calls

8 calls:

7.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
7.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
6.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
6.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
0.0ms	(*.f64 x (+.f64 y z))

series919.0ms (12.7%)

Counts

4 → 74

Calls

4 calls:

307.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
297.0ms	(cbrt.f64 (+.f64 (.f64 x (+.f64 y z)) (.f64 y z)))
161.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))
154.0ms	(+.f64 (.f64 x (+.f64 y z)) (.f64 y z))

Compiler

Compiled 4398 to 3166 computations (28% saved)

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4982	3204
1	4982	3204

prune147.0ms (2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	126	16	142

Error

20.4b

Counts

142 → 16

Compiler

Compiled 4206 to 977 computations (76.8% saved)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	341	1323
1	341	1323

regimes230.0ms (3.2%)

Compiler: Compiled 2571 to 1587 computations (38.3% saved)

bsearch0.0ms (0%)

regimes62.0ms (0.9%)

Compiler: Compiled 258 to 297 computations (-15.1% saved)

bsearch0.0ms (0%)

regimes115.0ms (1.6%)

Compiler: Compiled 222 to 267 computations (-20.3% saved)

bsearch55.0ms (0.8%)

Steps

Iters	Range		Point
7	3.913867651201436e-80	7.485197217766062e-78	1.635172749338751e-78
10	-8.805526979101948e-54	-2.9237242746137065e-70	-1.0909387547066737e-60

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes111.0ms (1.5%)

Compiler: Compiled 192 to 240 computations (-25% saved)

bsearch61.0ms (0.8%)

Steps

Iters	Range		Point
7	3.913867651201436e-80	7.485197217766062e-78	7.667442526895369e-80
10	-8.805526979101948e-54	-2.9237242746137065e-70	-5.95166002403931e-63

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes105.0ms (1.5%)

Compiler: Compiled 162 to 213 computations (-31.5% saved)

bsearch61.0ms (0.8%)

Steps

Iters	Range		Point
7	3.913867651201436e-80	7.485197217766062e-78	1.635172749338751e-78
10	-8.805526979101948e-54	-2.9237242746137065e-70	-4.2385012975540664e-63

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes87.0ms (1.2%)

Compiler: Compiled 114 to 165 computations (-44.7% saved)

bsearch36.0ms (0.5%)

Steps

Iters	Range		Point
6	8.777541458364104e-103	5.719721191578017e-102	8.869467189010179e-103
5	-1.3801093157521383e-154	-3.6506696387943448e-155	-6.990668740168875e-155

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes131.0ms (1.8%)

Compiler: Compiled 90 to 141 computations (-56.7% saved)

bsearch127.0ms (1.8%)

Steps

Iters	Range		Point
7	8.737776908891173e+151	1.4489347735988193e+153	1.6803814448151945e+152
6	1.2316178374976896e+88	5.018328115712778e+88	1.3955801900230308e+88
7	8294534240.1937475	263180186603.21533	190939381238.06134
6	8.777541458364104e-103	5.719721191578017e-102	2.1086282288358978e-102
11	-4.088997493895085e-103	-2.0337999321450308e-125	-4.7406987062430046e-117

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes88.0ms (1.2%)

Compiler: Compiled 72 to 120 computations (-66.7% saved)

bsearch54.0ms (0.8%)

Steps

Iters	Range		Point
10	6.314547775866411e-54	1.5966754188874746e-42	7.573413720986405e-49
7	-3.42597936803379e-78	-1.6459167129524782e-80	-5.215090713437783e-79

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes33.0ms (0.5%)

Compiler: Compiled 54 to 99 computations (-83.3% saved)

bsearch0.0ms (0%)

regimes30.0ms (0.4%)

Accuracy

Total 1.0b remaining (4.7%)

Threshold costs 1.0b (4.7%)

Compiler

Compiled 36 to 78 computations (-116.7% saved)

bsearch13.0ms (0.2%)

Compiler: Compiled 245 to 174 computations (29% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	126	314
1	126	314

end0.0ms (0%)

sample1.7s (23%)

Algorithm

1×

intervals

Results

358.0ms	8000×	body	128	valid
95.0ms	2285×	body	128	nan

Compiler

Compiled 1143 to 752 computations (34.2% saved)

Pareto

-0.5559563343758767

Details

analyze452.0ms (6.3%)

sample26.0ms (0.4%)

simplify93.0ms (1.3%)

prune9.0ms (0.1%)

localize9.0ms (0.1%)

rewrite23.0ms (0.3%)

series390.0ms (5.4%)

simplify79.0ms (1.1%)

prune136.0ms (1.9%)

localize14.0ms (0.2%)

rewrite32.0ms (0.4%)

series624.0ms (8.6%)

simplify63.0ms (0.9%)

prune135.0ms (1.9%)

localize18.0ms (0.3%)

rewrite30.0ms (0.4%)

series642.0ms (8.9%)

simplify64.0ms (0.9%)

prune126.0ms (1.7%)

localize12.0ms (0.2%)

rewrite32.0ms (0.4%)

series919.0ms (12.7%)

simplify54.0ms (0.7%)

prune147.0ms (2%)

simplify19.0ms (0.3%)

regimes230.0ms (3.2%)

bsearch0.0ms (0%)

regimes62.0ms (0.9%)

bsearch0.0ms (0%)

regimes115.0ms (1.6%)

bsearch55.0ms (0.8%)

regimes111.0ms (1.5%)

bsearch61.0ms (0.8%)

regimes105.0ms (1.5%)

bsearch61.0ms (0.8%)

regimes87.0ms (1.2%)

bsearch36.0ms (0.5%)

regimes131.0ms (1.8%)

bsearch127.0ms (1.8%)

regimes88.0ms (1.2%)

bsearch54.0ms (0.8%)

regimes33.0ms (0.5%)

bsearch0.0ms (0%)

regimes30.0ms (0.4%)

bsearch13.0ms (0.2%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample1.7s (23%)

Profiling