Details

analyze51.0ms (1.5%)

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
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample15.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	5×	body	128	nan
0.0ms	3×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify101.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	207	12
1	207	12

prune3.0ms (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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.3b	(*.f64 y (sqrt.f64 x))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_3169`
7×	`add-log-exp_binary64_3186`
6×	`-un-lft-identity_binary64_3147` `associate-r*_binary64_3087` `add-cube-cbrt_binary64_3182`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `associate-+l+_binary64_3080` `pow1_binary64_3208` `sqrt-prod_binary64_3163`
3×	`cancel-sign-sub-inv_binary64_3113` `associate-l_binary64_3088`
2×	`unswap-sqr_binary64_3115` `sum-log_binary64_3238`
1×	`*-commutative_binary64_3078` `associate-+l-_binary64_3082` `flip-+_binary64_3121` `pow-prod-down_binary64_3218` `flip3-+_binary64_3150` `sub-neg_binary64_3140` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `diff-log_binary64_3239`

Counts

2 → 39

Calls

2 calls:

9.0ms	(*.f64 y (sqrt.f64 x))
7.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

series111.0ms (3.2%)

Counts

2 → 15

Calls

2 calls:

62.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
48.0ms	(*.f64 y (sqrt.f64 x))

Compiler

Compiled 239 to 220 computations (7.9% saved)

simplify60.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5031	558

prune49.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	9	55

Merged error: 0.0b

Counts

55 → 9

Compiler

Compiled 722 to 350 computations (51.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_3163`
25×	`add-sqr-sqrt_binary64_3169`
18×	`associate-r_binary64_3087`
15×	`*-un-lft-identity_binary64_3147` `pow1_binary64_3208` `add-cube-cbrt_binary64_3182`
11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
8×	`sqrt-pow1_binary64_3165`
4×	`pow-prod-down_binary64_3218` `rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `pow1/2_binary64_3227` `cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186` `associate-l_binary64_3088`
3×	`unswap-sqr_binary64_3115`
2×	`*-commutative_binary64_3078`

Counts

4 → 88

Calls

4 calls:

10.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series338.0ms (9.6%)

Counts

4 → 18

Calls

4 calls:

171.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
59.0ms	(sqrt.f64 (sqrt.f64 x))
58.0ms	(sqrt.f64 (sqrt.f64 x))
50.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

Compiler

Compiled 491 to 425 computations (13.4% saved)

simplify107.0ms (3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4883	892
1	4883	892

prune92.0ms (2.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	106	9	115

Merged error: 0.0b

Counts

115 → 9

Compiler

Compiled 1742 to 677 computations (61.1% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`sqrt-prod_binary64_3163`
32×	`add-sqr-sqrt_binary64_3169`
25×	`associate-r_binary64_3087`
21×	`unpow-prod-down_binary64_3226`
20×	`*-un-lft-identity_binary64_3147` `add-exp-log_binary64_3185` `add-cube-cbrt_binary64_3182`
13×	`sqrt-pow1_binary64_3165`
12×	`pow1_binary64_3208`
11×	`add-cbrt-cube_binary64_3183`
10×	`prod-exp_binary64_3196`
5×	`unswap-sqr_binary64_3115` `pow1/2_binary64_3227` `pow-pow_binary64_3219`
4×	`cbrt-unprod_binary64_3180` `add-log-exp_binary64_3186` `associate-l_binary64_3088`
3×	`pow-exp_binary64_3215` `pow-to-exp_binary64_3216` `sqr-pow_binary64_3119` `rem-sqrt-square_binary64_3160` `pow-unpow_binary64_3224`
2×	`*-commutative_binary64_3078`
1×	`pow-prod-down_binary64_3218` `sqrt-pow2_binary64_3166`

Counts

4 → 114

Calls

4 calls:

12.0ms	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))
9.0ms	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3/2))
4.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3/2)
3.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 x)))

series459.0ms (13.1%)

Counts

4 → 18

Calls

4 calls:

223.0ms	(*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3/2))
114.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3/2)
65.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 x)))
57.0ms	(.f64 (.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 x))))

Compiler

Compiled 566 to 500 computations (11.7% saved)

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4940	1462
1	4940	1462

prune131.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	133	8	141

Merged error: 0.0b

Counts

141 → 8

Compiler

Compiled 2555 to 1214 computations (52.5% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x))))
0.5b	(cbrt.f64 x)
0.5b	(cbrt.f64 x)

rewrite32.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `associate-r_binary64_3087` `pow1_binary64_3208` `sqrt-prod_binary64_3163`
12×	`*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182`
9×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `cbrt-prod_binary64_3178`
4×	`add-log-exp_binary64_3186`
2×	`-commutative_binary64_3078` `pow1/3_binary64_3229` `associate-l*_binary64_3088`

Counts

4 → 73

Calls

4 calls:

14.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
8.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series679.0ms (19.3%)

Counts

4 → 18

Calls

4 calls:

248.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
232.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x))))
100.0ms	(cbrt.f64 x)
98.0ms	(cbrt.f64 x)

Compiler

Compiled 813 to 711 computations (12.5% saved)

simplify84.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4908	1591
1	4908	1591

prune83.0ms (2.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Merged error: 0.0b

Counts

99 → 8

Compiler

Compiled 2059 to 625 computations (69.6% saved)

regimes124.0ms (3.5%)

Compiler: Compiled 1115 to 802 computations (28.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample785.0ms (22.3%)

Algorithm

1×

intervals

Results

260.0ms	7996×	body	128	valid
4.0ms	132×	body	128	nan
2.0ms	61×	body	128	invalid
0.0ms	3×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 382 to 277 computations (27.5% saved)

Details

analyze51.0ms (1.5%)

sample15.0ms (0.4%)

simplify101.0ms (2.9%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

rewrite20.0ms (0.6%)

series111.0ms (3.2%)

simplify60.0ms (1.7%)

prune49.0ms (1.4%)

localize8.0ms (0.2%)

rewrite28.0ms (0.8%)

series338.0ms (9.6%)

simplify107.0ms (3%)

prune92.0ms (2.6%)

localize12.0ms (0.4%)

rewrite43.0ms (1.2%)

series459.0ms (13.1%)

simplify76.0ms (2.2%)

prune131.0ms (3.7%)

localize15.0ms (0.4%)

rewrite32.0ms (0.9%)

series679.0ms (19.3%)

simplify84.0ms (2.4%)

prune83.0ms (2.4%)

regimes124.0ms (3.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample785.0ms (22.3%)

Profiling