Details

analyze382.0ms (5.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7544	20
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify292.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (287.0ms)

Iter	Nodes	Cost
0	7544	20

prune2.0ms (0%)

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 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)

rewrite200.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

66×	`*-un-lft-identity_binary64_3829`
50×	`times-frac_binary64_3835`
43×	`add-sqr-sqrt_binary64_3851`
31×	`add-cube-cbrt_binary64_3864` `sqrt-prod_binary64_3845`
16×	`distribute-lft-out_binary64_3780`
15×	`log-prod_binary64_3915`
13×	`div-inv_binary64_3826`
10×	`difference-of-squares_binary64_3798`
8×	`associate-/l*_binary64_3774`
7×	`add-exp-log_binary64_3867`
6×	`pow1_binary64_3890` `add-log-exp_binary64_3868` `add-cbrt-cube_binary64_3865` `distribute-rgt-out_binary64_3782`
4×	`sqrt-div_binary64_3846`
3×	`associate-/r*_binary64_3773` `log-div_binary64_3916`
2×	`flip3--_binary64_3833` `associate-/l/_binary64_3776` `flip--_binary64_3804` `frac-add_binary64_3837` `flip3-+_binary64_3832` `flip-+_binary64_3803` `distribute-rgt1-in_binary64_3785`
1×	`div-exp_binary64_3880` `cbrt-undiv_binary64_3863` `frac-2neg_binary64_3840` `clear-num_binary64_3828` `sum-log_binary64_3920` `+-commutative_binary64_3759` `log-pow_binary64_3918` `rem-log-exp_binary64_3870` `pow1/2_binary64_3909` `sqrt-pow1_binary64_3847` `rem-sqrt-square_binary64_3842`

Counts

4 → 117

Calls

4 calls:

22.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
22.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 2629 to 1663 computations (36.7% saved)

series171.0ms (2.5%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

51.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
39.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
35.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
26.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 699 to 601 computations (14% saved)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5069	2713

prune146.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	2	142

Error

Counts

142 → 2

Compiler

Compiled 2640 to 1703 computations (35.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.3b	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x))
0.3b	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x))
0.5b	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 x)) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x)))

rewrite2.2s (32.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

1056×	`sqrt-prod_binary64_3845`
687×	`add-sqr-sqrt_binary64_3851`
620×	`times-frac_binary64_3835`
339×	`*-un-lft-identity_binary64_3829`
296×	`add-cube-cbrt_binary64_3864`
140×	`swap-sqr_binary64_3796`
86×	`difference-of-squares_binary64_3798`
70×	`associate-l_binary64_3770` `associate-r_binary64_3769`
49×	`unswap-sqr_binary64_3797`
22×	`associate-/l*_binary64_3774`
20×	`add-exp-log_binary64_3867` `add-cbrt-cube_binary64_3865`
13×	`pow1_binary64_3890`
12×	`sqrt-div_binary64_3846` `associate-/r*_binary64_3773`
6×	`div-exp_binary64_3880` `cbrt-undiv_binary64_3863` `sqrt-undiv_binary64_3850` `div-inv_binary64_3826`
4×	`prod-exp_binary64_3878` `add-log-exp_binary64_3868` `cbrt-unprod_binary64_3862` `associate-/l/_binary64_3776` `sqrt-pow1_binary64_3847`
3×	`flip3--_binary64_3833` `flip--_binary64_3804`
2×	`frac-2neg_binary64_3840` `clear-num_binary64_3828` `pow1/2_binary64_3909` `rem-sqrt-square_binary64_3842`
1×	`pow2_binary64_3910` `pow-prod-down_binary64_3900` `pow-prod-up_binary64_3899` `pow-plus_binary64_3892` `sqrt-unprod_binary64_3849` `rem-square-sqrt_binary64_3841` `frac-times_binary64_3839` `pow-sqr_binary64_3802` `associate-l/_binary64_3772` `associate-r/_binary64_3771` `*-commutative_binary64_3760`

Counts

4 → 574

Calls

4 calls:

94.0ms	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 x)) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x)))
9.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x))
9.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x))
4.0ms	(sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))

Compiler

Compiled 25448 to 14708 computations (42.2% saved)

series202.0ms (3%)

Error

Counts

4 → 18

Calls

4 calls:

55.0ms	(sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))))
46.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x))
41.0ms	(.f64 (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))) (sqrt.f64 x)) (/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x)))
39.0ms	(/.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x))

Compiler

Compiled 1223 to 974 computations (20.4% saved)

simplify246.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

592 → 592

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4961	19013
1	4961	19013

prune1.4s (19.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	592	0	592
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	592	2	594

Error

Counts

594 → 2

Compiler

Compiled 19893 to 11122 computations (44.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))))
0.0b	(log.f64 (/.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))) (*.f64 x x)))
0.0b	(.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))
30.5b	(/.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))) (*.f64 x x))

rewrite115.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

17×	`add-exp-log_binary64_3867`
16×	`add-sqr-sqrt_binary64_3851`
12×	`*-un-lft-identity_binary64_3829`
11×	`add-cbrt-cube_binary64_3865` `add-cube-cbrt_binary64_3864`
8×	`associate-r_binary64_3769`
7×	`pow1_binary64_3890` `log-prod_binary64_3915`
6×	`add-log-exp_binary64_3868` `times-frac_binary64_3835` `sqrt-prod_binary64_3845`
4×	`div-exp_binary64_3880`
3×	`prod-exp_binary64_3878` `associate-/l_binary64_3774` `associate-l*_binary64_3770` `rem-log-exp_binary64_3870`
2×	`cbrt-undiv_binary64_3863` `cbrt-unprod_binary64_3862` `div-inv_binary64_3826` `flip3-+_binary64_3832` `associate-/l/_binary64_3776` `flip-+_binary64_3803` `unswap-sqr_binary64_3797` `sqrt-div_binary64_3846` `associate-*r/_binary64_3771` `difference-of-squares_binary64_3798`
1×	`frac-2neg_binary64_3840` `clear-num_binary64_3828` `associate-/r_binary64_3773` `pow-prod-down_binary64_3900` `flip3--_binary64_3833` `flip--_binary64_3804` `-commutative_binary64_3760` `log-pow_binary64_3918` `log-div_binary64_3916` `sum-log_binary64_3920` `+-commutative_binary64_3759`

Counts

4 → 79

Calls

4 calls:

9.0ms	(.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))
6.0ms	(/.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))) (*.f64 x x))
5.0ms	(log.f64 (/.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))) (*.f64 x x)))
3.0ms	(+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))))

Compiler

Compiled 2042 to 1073 computations (47.5% saved)

series168.0ms (2.5%)

Error

Counts

4 → 24

Calls

4 calls:

49.0ms	(log.f64 (/.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))) (*.f64 x x)))
36.0ms	(/.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))) (*.f64 x x))
36.0ms	(.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))
26.0ms	(+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))))

Compiler

Compiled 727 to 578 computations (20.5% saved)

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5214	1847

prune100.0ms (1.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	103	2	105

Error

Counts

105 → 2

Compiler

Compiled 1949 to 1151 computations (40.9% saved)

regimes111.0ms (1.6%)

Accuracy

Total 0.0b remaining (94.7%)

Threshold costs 0.0b (94.7%)

Compiler

Compiled 818 to 623 computations (23.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	42
1	32	42

end0.0ms (0%)

sample890.0ms (13.1%)

Algorithm

1×

intervals

Results

425.0ms	8000×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 260 to 197 computations (24.2% saved)

Details

analyze382.0ms (5.6%)

sample20.0ms (0.3%)

simplify292.0ms (4.3%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite200.0ms (2.9%)

series171.0ms (2.5%)

simplify89.0ms (1.3%)

prune146.0ms (2.1%)

localize12.0ms (0.2%)

rewrite2.2s (32.3%)

series202.0ms (3%)

simplify246.0ms (3.6%)

prune1.4s (19.9%)

localize9.0ms (0.1%)

rewrite115.0ms (1.7%)

series168.0ms (2.5%)

simplify81.0ms (1.2%)

prune100.0ms (1.5%)

regimes111.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample890.0ms (13.1%)

Profiling