Details

analyze300.0ms (8.2%)

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
6.2%	93.6%	0.1%	6
15.6%	84.3%	0.1%	7
23.4%	76.5%	0.1%	8
33.5%	63.2%	3.3%	9
43.3%	49.5%	7.2%	10
48.2%	43.9%	7.9%	11
54.5%	34.2%	11.3%	12
60.6%	25.6%	13.8%	13
63.1%	22.8%	14.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample16.0ms (0.4%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
1.0ms	27×	body	128	invalid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify111.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	301	10
1	301	10

prune4.0ms (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

0.0b

Counts

2 → 2

Compiler

Compiled 23 to 20 computations (13% saved)

localize5.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 y (-.f64 x z))
0.0b	(+.f64 z (*.f64 y (-.f64 x z)))
0.0b	(+.f64 z (*.f64 y (-.f64 x z)))
0.0b	(*.f64 y (-.f64 x z))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cancel-sign-sub-inv_binary64_12661` `add-sqr-sqrt_binary64_12717`
10×	`*-un-lft-identity_binary64_12695`
8×	`add-cube-cbrt_binary64_12730` `distribute-rgt-in_binary64_12645` `associate-+r+_binary64_12627` `distribute-lft-in_binary64_12644`
5×	`associate-r_binary64_12635`
4×	`add-exp-log_binary64_12733` `sub-neg_binary64_12688` `pow1_binary64_12756` `add-log-exp_binary64_12734` `add-cbrt-cube_binary64_12731`
3×	`associate-l_binary64_12636`
2×	`associate-*r/_binary64_12637`
1×	`prod-exp_binary64_12744` `distribute-lft-out--_binary64_12647` `flip3--_binary64_12699` `flip-+_binary64_12669` `pow-prod-down_binary64_12766` `*-commutative_binary64_12626` `difference-of-squares_binary64_12664` `flip--_binary64_12670` `flip3-+_binary64_12698` `sum-log_binary64_12786` `unswap-sqr_binary64_12663` `+-commutative_binary64_12625` `cbrt-unprod_binary64_12728`

Counts

2 → 49

Calls

4 calls:

8.0ms	(*.f64 y (-.f64 x z))
5.0ms	(+.f64 z (*.f64 y (-.f64 x z)))
0.0ms	(+.f64 z (*.f64 y (-.f64 x z)))
0.0ms	(*.f64 y (-.f64 x z))

series218.0ms (5.9%)

Counts

2 → 33

Calls

2 calls:

119.0ms	(+.f64 z (*.f64 y (-.f64 x z)))
99.0ms	(*.f64 y (-.f64 x z))

Compiler

Compiled 387 to 328 computations (15.2% saved)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4909	764
1	4909	764

prune45.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

Counts

84 → 3

Compiler

Compiled 828 to 172 computations (79.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (-.f64 1 y))
0.0b	(+.f64 (.f64 x y) (.f64 z (-.f64 1 y)))
0.0b	(*.f64 z (-.f64 1 y))
0.0b	(+.f64 (.f64 x y) (.f64 z (-.f64 1 y)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_12717`
12×	`cancel-sign-sub-inv_binary64_12661`
11×	`*-un-lft-identity_binary64_12695`
8×	`add-cube-cbrt_binary64_12730` `distribute-rgt-in_binary64_12645` `associate-+r+_binary64_12627` `distribute-lft-in_binary64_12644`
6×	`associate-r_binary64_12635`
4×	`add-exp-log_binary64_12733` `sub-neg_binary64_12688` `pow1_binary64_12756` `add-log-exp_binary64_12734` `add-cbrt-cube_binary64_12731`
3×	`associate-l_binary64_12636`
2×	`difference-of-squares_binary64_12664` `associate-*r/_binary64_12637`
1×	`prod-exp_binary64_12744` `distribute-lft-out--_binary64_12647` `flip3--_binary64_12699` `flip-+_binary64_12669` `pow-prod-down_binary64_12766` `*-commutative_binary64_12626` `flip--_binary64_12670` `flip3-+_binary64_12698` `sum-log_binary64_12786` `unswap-sqr_binary64_12663` `+-commutative_binary64_12625` `cbrt-unprod_binary64_12728`

Counts

2 → 50

Calls

4 calls:

9.0ms	(*.f64 z (-.f64 1 y))
6.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 1 y)))
0.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 1 y)))
0.0ms	(*.f64 z (-.f64 1 y))

series185.0ms (5%)

Counts

2 → 27

Calls

2 calls:

126.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 1 y)))
58.0ms	(*.f64 z (-.f64 1 y))

Compiler

Compiled 332 to 283 computations (14.8% saved)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5326	712

prune44.0ms (1.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	77	3	80

Error

Counts

80 → 3

Compiler

Compiled 864 to 308 computations (64.4% saved)

localize10.0ms (0.3%)

Local error

Found 8 expressions with local error:

16.9b	(/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z))
10.3b	(.f64 y (-.f64 (.f64 x x) (*.f64 z z)))
2.3b	(-.f64 (.f64 x x) (.f64 z z))
0.0b	(+.f64 z (/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z)))
0.0b	(+.f64 z (/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z)))
2.3b	(-.f64 (.f64 x x) (.f64 z z))
10.3b	(.f64 y (-.f64 (.f64 x x) (*.f64 z z)))
16.9b	(/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z))

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_12695`
11×	`add-exp-log_binary64_12733` `add-cbrt-cube_binary64_12731`
10×	`add-sqr-sqrt_binary64_12717`
8×	`add-cube-cbrt_binary64_12730` `add-log-exp_binary64_12734`
6×	`pow1_binary64_12756`
4×	`associate-/r_binary64_12639` `associate-r_binary64_12635` `times-frac_binary64_12701` `associate-r/_binary64_12637`
3×	`distribute-lft-out_binary64_12646` `associate-l_binary64_12636` `cancel-sign-sub-inv_binary64_12661` `flip3--_binary64_12699` `flip--_binary64_12670` `sub-neg_binary64_12688`
2×	`prod-exp_binary64_12744` `div-exp_binary64_12746` `cbrt-undiv_binary64_12729` `associate-/r/_binary64_12641` `associate-/l/_binary64_12642` `flip-+_binary64_12669` `difference-of-squares_binary64_12664` `distribute-rgt-in_binary64_12645` `flip3-+_binary64_12698` `cbrt-unprod_binary64_12728` `distribute-lft-in_binary64_12644`
1×	`diff-log_binary64_12787` `associate-/l_binary64_12640` `frac-2neg_binary64_12706` `div-inv_binary64_12692` `pow-prod-down_binary64_12766` `-commutative_binary64_12626` `sum-log_binary64_12786` `unswap-sqr_binary64_12663` `+-commutative_binary64_12625` `clear-num_binary64_12694`

Counts

4 → 77

Calls

8 calls:

12.0ms	(/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z))
9.0ms	(+.f64 z (/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z)))
8.0ms	(.f64 y (-.f64 (.f64 x x) (*.f64 z z)))
5.0ms	(-.f64 (.f64 x x) (.f64 z z))
0.0ms	(+.f64 z (/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z)))

series883.0ms (24%)

Counts

4 → 60

Calls

4 calls:

378.0ms	(+.f64 z (/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z)))
234.0ms	(/.f64 (.f64 y (-.f64 (.f64 x x) (*.f64 z z))) (+.f64 x z))
173.0ms	(.f64 y (-.f64 (.f64 x x) (*.f64 z z)))
98.0ms	(-.f64 (.f64 x x) (.f64 z z))

Compiler

Compiled 1149 to 912 computations (20.6% saved)

simplify68.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4988	1669
1	4988	1669

prune81.0ms (2.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	137	3	140

Error

Counts

140 → 3

Compiler

Compiled 2000 to 334 computations (83.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	80	104
1	80	104

regimes91.0ms (2.5%)

Compiler: Compiled 338 to 358 computations (-5.9% saved)

bsearch0.0ms (0%)

regimes86.0ms (2.3%)

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

bsearch26.0ms (0.7%)

Steps

Iters	Range		Point
8	0.5953348852832063	194.84011144333917	0.9940110682950706
8	-5396168138.288328	-255039.89946208967	-258703.41134348375

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes106.0ms (2.9%)

Compiler: Compiled 57 to 105 computations (-84.2% saved)

bsearch21.0ms (0.6%)

Steps

Iters	Range		Point
7	8.524612368085428e-41	8.878806186440847e-39	6.892771576116899e-39
6	-1.42608262710057e-05	-1.8142275936444912e-06	-1.1254590216590106e-05

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes134.0ms (3.6%)

Compiler: Compiled 42 to 90 computations (-114.3% saved)

bsearch21.0ms (0.6%)

Steps

Iters	Range		Point
7	8.524612368085428e-41	8.878806186440847e-39	7.503859148524268e-39
6	-1.42608262710057e-05	-1.8142275936444912e-06	-1.8363322705151943e-06

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes103.0ms (2.8%)

Compiler: Compiled 27 to 75 computations (-177.8% saved)

bsearch20.0ms (0.6%)

Steps

Iters	Range		Point
7	8.524612368085428e-41	8.878806186440847e-39	4.8702615084312675e-40
6	-1.42608262710057e-05	-1.8142275936444912e-06	-1.8363322705151943e-06

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.8%)

Compiler: Compiled 18 to 63 computations (-250% saved)

bsearch0.0ms (0%)

regimes27.0ms (0.7%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes22.0ms (0.6%)

Accuracy

Total 0.0b remaining (66%)

Threshold costs 0.0b (66%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch9.0ms (0.2%)

Compiler: Compiled 90 to 64 computations (28.9% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	110
1	80	110

end0.0ms (0%)

sample747.0ms (20.3%)

Algorithm

1×

intervals

Results

225.0ms	8000×	body	128	valid
22.0ms	709×	body	128	invalid

Compiler

Compiled 164 to 158 computations (3.7% saved)

Pareto

0.20716927893395337

Details

analyze300.0ms (8.2%)

sample16.0ms (0.4%)

simplify111.0ms (3%)

prune4.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.4%)

series218.0ms (5.9%)

simplify84.0ms (2.3%)

prune45.0ms (1.2%)

localize8.0ms (0.2%)

rewrite18.0ms (0.5%)

series185.0ms (5%)

simplify84.0ms (2.3%)

prune44.0ms (1.2%)

localize10.0ms (0.3%)

rewrite41.0ms (1.1%)

series883.0ms (24%)

simplify68.0ms (1.9%)

prune81.0ms (2.2%)

simplify4.0ms (0.1%)

regimes91.0ms (2.5%)

bsearch0.0ms (0%)

regimes86.0ms (2.3%)

bsearch26.0ms (0.7%)

regimes106.0ms (2.9%)

bsearch21.0ms (0.6%)

regimes134.0ms (3.6%)

bsearch21.0ms (0.6%)

regimes103.0ms (2.8%)

bsearch20.0ms (0.6%)

regimes30.0ms (0.8%)

bsearch0.0ms (0%)

regimes27.0ms (0.7%)

bsearch0.0ms (0%)

regimes22.0ms (0.6%)

bsearch9.0ms (0.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample747.0ms (20.3%)

Profiling