Details

analyze52.0ms (1.1%)

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

Compiler

Compiled 15 to 14 computations (6.7% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
0.0ms	6×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 29 to 29 computations (0% saved)

simplify230.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	1583	18
1	1583	18

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

0.3b

Counts

2 → 2

Compiler

Compiled 38 to 35 computations (7.9% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.6b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(*.f64 3 (sqrt.f64 x))
0.6b	(/.f64 1 (*.f64 x 9))

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64_13718`
22×	`add-exp-log_binary64_13756`
20×	`add-sqr-sqrt_binary64_13740`
16×	`add-cbrt-cube_binary64_13754`
15×	`associate-r_binary64_13658`
14×	`pow1_binary64_13779`
12×	`add-cube-cbrt_binary64_13753`
7×	`prod-exp_binary64_13767`
6×	`add-log-exp_binary64_13757` `cancel-sign-sub-inv_binary64_13684`
5×	`distribute-lft-in_binary64_13667` `distribute-rgt-in_binary64_13668` `pow-prod-down_binary64_13789` `cbrt-unprod_binary64_13751`
4×	`distribute-lft-out_binary64_13669` `associate-l_binary64_13659` `div-exp_binary64_13769` `sqrt-prod_binary64_13734`
3×	`times-frac_binary64_13724` `associate-/l*_binary64_13663` `distribute-lft-out--_binary64_13670` `div-inv_binary64_13715`
2×	`rec-exp_binary64_13768` `associate-r/_binary64_13660` `difference-of-squares_binary64_13687` `-commutative_binary64_13649` `1-exp_binary64_13762` `sub-neg_binary64_13711` `unswap-sqr_binary64_13686` `pow-flip_binary64_13792` `cbrt-undiv_binary64_13752` `associate--l+_binary64_13655`
1×	`associate-/r*_binary64_13662` `frac-2neg_binary64_13729` `flip3-+_binary64_13721` `difference-of-sqr-1_binary64_13688` `sum-log_binary64_13809` `+-commutative_binary64_13648` `flip-+_binary64_13692` `flip3--_binary64_13722` `flip--_binary64_13693` `clear-num_binary64_13717` `inv-pow_binary64_13803`

Counts

4 → 99

Calls

8 calls:

22.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
6.0ms	(*.f64 3 (sqrt.f64 x))
6.0ms	(/.f64 1 (*.f64 x 9))
5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))

series239.0ms (4.8%)

Counts

4 → 27

Calls

4 calls:

138.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
67.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
17.0ms	(/.f64 1 (*.f64 x 9))
16.0ms	(*.f64 3 (sqrt.f64 x))

Compiler

Compiled 644 to 583 computations (9.5% saved)

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	4922	1421
1	4922	1421

prune175.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	118	10	128

Error

0.0b

Counts

128 → 10

Compiler

Compiled 2211 to 1602 computations (27.5% saved)

localize11.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.1b	(sqrt.f64 (/.f64 1 x))
0.0b	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
0.1b	(sqrt.f64 (/.f64 1 x))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_13740`
33×	`sqrt-prod_binary64_13734`
28×	`*-un-lft-identity_binary64_13718`
24×	`add-cube-cbrt_binary64_13753`
22×	`times-frac_binary64_13724` `associate-r_binary64_13658`
15×	`pow1_binary64_13779`
13×	`add-cbrt-cube_binary64_13754` `add-exp-log_binary64_13756`
12×	`associate-l_binary64_13659`
7×	`associate-*r/_binary64_13660`
6×	`unswap-sqr_binary64_13686`
5×	`prod-exp_binary64_13767` `distribute-lft-in_binary64_13667` `distribute-rgt-in_binary64_13668` `pow-prod-down_binary64_13789` `cbrt-unprod_binary64_13751`
4×	`add-log-exp_binary64_13757`
3×	`*-commutative_binary64_13649` `rem-sqrt-square_binary64_13731` `sqrt-pow1_binary64_13736`
2×	`flip3-+_binary64_13721` `sqrt-div_binary64_13735` `flip-+_binary64_13692` `div-inv_binary64_13715`
1×	`difference-of-sqr--1_binary64_13689` `distribute-lft-out_binary64_13669` `pow1/2_binary64_13798` `pow-flip_binary64_13792` `inv-pow_binary64_13803`

Counts

4 → 115

Calls

8 calls:

9.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
9.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
8.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
3.0ms	(sqrt.f64 (/.f64 1 x))
0.0ms	(+.f64 (.f64 1/3 (sqrt.f64 (/.f64 1 x))) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))

series204.0ms (4.1%)

Counts

4 → 24

Calls

4 calls:

90.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
77.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
22.0ms	(*.f64 1/3 (sqrt.f64 (/.f64 1 x)))
14.0ms	(sqrt.f64 (/.f64 1 x))

Compiler

Compiled 788 to 680 computations (13.7% saved)

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4981	1541
1	4981	1541

prune163.0ms (3.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	140	9	149

Error

0.0b

Counts

149 → 9

Compiler

Compiled 2799 to 2059 computations (26.4% saved)

localize12.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(*.f64 1/3 (pow.f64 x -1/2))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.0b	(+.f64 (.f64 1/3 (pow.f64 x -1/2)) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
0.0b	(+.f64 (.f64 1/3 (pow.f64 x -1/2)) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b	(*.f64 1/3 (pow.f64 x -1/2))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_13740`
16×	`add-exp-log_binary64_13756`
13×	`add-cbrt-cube_binary64_13754` `associate-r_binary64_13658` `*-un-lft-identity_binary64_13718`
12×	`associate-l_binary64_13659`
11×	`pow1_binary64_13779` `add-cube-cbrt_binary64_13753`
9×	`distribute-lft-in_binary64_13667` `distribute-rgt-in_binary64_13668`
7×	`prod-exp_binary64_13767`
6×	`associate-*r/_binary64_13660` `add-log-exp_binary64_13757`
5×	`unswap-sqr_binary64_13686` `cbrt-unprod_binary64_13751`
4×	`associate-+r+_binary64_13650` `unpow-prod-down_binary64_13797` `pow-prod-down_binary64_13789` `sqrt-prod_binary64_13734`
3×	`*-commutative_binary64_13649` `flip3-+_binary64_13721` `flip-+_binary64_13692`
2×	`sqr-pow_binary64_13690`
1×	`difference-of-sqr--1_binary64_13689` `distribute-lft-out_binary64_13669` `sum-log_binary64_13809` `pow-exp_binary64_13786` `+-commutative_binary64_13648` `pow-to-exp_binary64_13787`

Counts

4 → 92

Calls

8 calls:

10.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
8.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
6.0ms	(+.f64 (.f64 1/3 (pow.f64 x -1/2)) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
5.0ms	(*.f64 1/3 (pow.f64 x -1/2))
0.0ms	(+.f64 (.f64 1/3 (pow.f64 x -1/2)) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))

series343.0ms (7%)

Counts

4 → 30

Calls

4 calls:

157.0ms	(+.f64 (.f64 1/3 (pow.f64 x -1/2)) (.f64 3 (*.f64 (sqrt.f64 x) (+.f64 y -1))))
97.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
73.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
17.0ms	(*.f64 1/3 (pow.f64 x -1/2))

Compiler

Compiled 897 to 764 computations (14.8% saved)

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4909	1623
1	4909	1623

prune140.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	122	9	131

Error

Counts

131 → 9

Compiler

Compiled 2324 to 1678 computations (27.8% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(/.f64 1/3 (sqrt.f64 x))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.0b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
0.0b	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
0.2b	(*.f64 (sqrt.f64 x) (+.f64 y -1))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
0.4b	(/.f64 1/3 (sqrt.f64 x))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_13740`
25×	`*-un-lft-identity_binary64_13718`
23×	`add-cube-cbrt_binary64_13753`
18×	`times-frac_binary64_13724`
16×	`sqrt-prod_binary64_13734`
13×	`add-cbrt-cube_binary64_13754` `add-exp-log_binary64_13756`
11×	`pow1_binary64_13779`
10×	`associate-*r/_binary64_13660`
9×	`distribute-lft-in_binary64_13667` `distribute-rgt-in_binary64_13668` `associate-l_binary64_13659`
6×	`associate-/r_binary64_13662` `add-log-exp_binary64_13757` `associate-r*_binary64_13658`
4×	`associate-+r+_binary64_13650` `flip3-+_binary64_13721` `prod-exp_binary64_13767` `pow-prod-down_binary64_13789` `cbrt-unprod_binary64_13751` `flip-+_binary64_13692`
3×	`associate-/l*_binary64_13663`
2×	`*-commutative_binary64_13649` `unswap-sqr_binary64_13686` `frac-add_binary64_13726`
1×	`frac-2neg_binary64_13729` `difference-of-sqr--1_binary64_13689` `distribute-lft-out_binary64_13669` `sum-log_binary64_13809` `+-commutative_binary64_13648` `div-exp_binary64_13769` `clear-num_binary64_13717` `cbrt-undiv_binary64_13752` `div-inv_binary64_13715`

Counts

4 → 108

Calls

8 calls:

11.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
8.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
8.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
4.0ms	(/.f64 1/3 (sqrt.f64 x))
0.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))

series342.0ms (6.9%)

Counts

4 → 30

Calls

4 calls:

161.0ms	(+.f64 (/.f64 1/3 (sqrt.f64 x)) (.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1))))
91.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 y -1)))
70.0ms	(*.f64 (sqrt.f64 x) (+.f64 y -1))
18.0ms	(/.f64 1/3 (sqrt.f64 x))

Compiler

Compiled 873 to 722 computations (17.3% saved)

simplify72.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5005	1920

prune145.0ms (2.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	139	8	147

Error

Counts

147 → 8

Compiler

Compiled 2367 to 1495 computations (36.8% saved)

simplify30.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	489	1581
1	489	1581

regimes205.0ms (4.2%)

Compiler: Compiled 2012 to 1756 computations (12.7% saved)

bsearch0.0ms (0%)

regimes70.0ms (1.4%)

Compiler: Compiled 494 to 466 computations (5.7% saved)

bsearch0.0ms (0%)

regimes67.0ms (1.4%)

Compiler: Compiled 442 to 422 computations (4.5% saved)

bsearch0.0ms (0%)

regimes41.0ms (0.8%)

Compiler: Compiled 186 to 194 computations (-4.3% saved)

bsearch0.0ms (0%)

regimes51.0ms (1%)

Compiler: Compiled 82 to 98 computations (-19.5% saved)

bsearch35.0ms (0.7%)

Steps

Iters	Range		Point
8	1.667813634533408e+113	4.0155884460378344e+117	1.8858905797142277e+113
8	-3.145880642405573e+35	-6.382690069926435e+31	-2.3300122767632005e+33

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes27.0ms (0.5%)

Compiler: Compiled 62 to 78 computations (-25.8% saved)

bsearch0.0ms (0%)

regimes24.0ms (0.5%)

Compiler: Compiled 46 to 62 computations (-34.8% saved)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

Compiler: Compiled 22 to 38 computations (-72.7% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.5%)

Compiler: Compiled 10 to 26 computations (-160% saved)

bsearch18.0ms (0.4%)

Steps

Iters	Range		Point
9	0.00014057311872385877	119.60066993930418	0.10999074355716452

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes14.0ms (0.3%)

Accuracy

Total 0.4b remaining (98.2%)

Threshold costs 0.4b (98.2%)

Compiler

Compiled 8 to 20 computations (-150% saved)

bsearch9.0ms (0.2%)

Compiler: Compiled 112 to 102 computations (8.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	167
1	63	167

end0.0ms (0%)

sample1.8s (35.8%)

Algorithm

1×

intervals

Results

375.0ms	8000×	body	128	valid
6.0ms	139×	body	128	nan
3.0ms	65×	body	128	invalid

Compiler

Compiled 1148 to 1006 computations (12.4% saved)

Pareto

0.07097683404047939

Details

analyze52.0ms (1.1%)

sample23.0ms (0.5%)

simplify230.0ms (4.7%)

prune5.0ms (0.1%)

localize10.0ms (0.2%)

rewrite48.0ms (1%)

series239.0ms (4.8%)

simplify43.0ms (0.9%)

prune175.0ms (3.6%)

localize11.0ms (0.2%)

rewrite40.0ms (0.8%)

series204.0ms (4.1%)

simplify68.0ms (1.4%)

prune163.0ms (3.3%)

localize12.0ms (0.2%)

rewrite37.0ms (0.7%)

series343.0ms (7%)

simplify84.0ms (1.7%)

prune140.0ms (2.8%)

localize8.0ms (0.2%)

rewrite39.0ms (0.8%)

series342.0ms (6.9%)

simplify72.0ms (1.5%)

prune145.0ms (2.9%)

simplify30.0ms (0.6%)

regimes205.0ms (4.2%)

bsearch0.0ms (0%)

regimes70.0ms (1.4%)

bsearch0.0ms (0%)

regimes67.0ms (1.4%)

bsearch0.0ms (0%)

regimes41.0ms (0.8%)

bsearch0.0ms (0%)

regimes51.0ms (1%)

bsearch35.0ms (0.7%)

regimes27.0ms (0.5%)

bsearch0.0ms (0%)

regimes24.0ms (0.5%)

bsearch0.0ms (0%)

regimes18.0ms (0.4%)

bsearch0.0ms (0%)

regimes22.0ms (0.5%)

bsearch18.0ms (0.4%)

regimes14.0ms (0.3%)

bsearch9.0ms (0.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.8s (35.8%)

Profiling