Details

analyze5.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample33.0ms (1.2%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify151.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	5204	47

prune10.0ms (0.3%)

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: 0.0b

Counts

2 → 2

Compiler

Compiled 125 to 77 computations (38.4% saved)

localize26.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`pow1_binary64`
35×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64` `pow-sqr_binary64` `pow2_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64` `pow3_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 107

Calls

4 calls:

13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series21.0ms (0.7%)

Counts

4 → 10

Calls

4 calls:

9.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify87.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5073	954

prune166.0ms (5.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	117	2	119

Merged error: 0.0b

Counts

119 → 2

Compiler

Compiled 7800 to 3083 computations (60.5% saved)

localize30.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite31.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`pow1_binary64`
35×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64` `pow-sqr_binary64` `pow2_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64` `pow3_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series21.0ms (0.8%)

Counts

4 → 10

Calls

4 calls:

9.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify89.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5077	924

prune195.0ms (6.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	117	2	119

Merged error: 0.0b

Counts

119 → 2

Compiler

Compiled 7257 to 3628 computations (50% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.3b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite34.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`associate-r_binary64`
18×	`times-frac_binary64`
16×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-/r_binary64` `associate-l*_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `cube-prod_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
2.0ms	(sqrt.f64 PI.f64)

series77.0ms (2.7%)

Counts

4 → 10

Calls

4 calls:

56.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
12.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
9.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.0ms	(sqrt.f64 PI.f64)

simplify82.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5167	3850

prune184.0ms (6.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	118	4	122

Merged error: 0b

Counts

122 → 4

Compiler

Compiled 4830 to 3204 computations (33.7% saved)

localize19.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.3b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite33.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
14×	`add-exp-log_binary64`
12×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64`
3×	`associate-l_binary64` `associate-/l*_binary64` `times-frac_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64` `unpow3_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 80

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series67.0ms (2.4%)

Counts

4 → 8

Calls

4 calls:

59.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify48.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5161	1997

prune113.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	88	4	92

Merged error: 0b

Counts

92 → 4

Compiler

Compiled 3532 to 2161 computations (38.8% saved)

regimes45.0ms (1.6%)

Compiler: Compiled 330 to 228 computations (30.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	94
1	49	94

end0.0ms (0%)

sample1.2s (42.8%)

Algorithm

1×

intervals

Results

738.0ms	8000×	body	80	valid
87.0ms	8000×	pre	80	true

Compiler

Compiled 289 to 174 computations (39.8% saved)

Details

analyze5.0ms (0.2%)

sample33.0ms (1.2%)

simplify151.0ms (5.3%)

prune10.0ms (0.3%)

localize26.0ms (0.9%)

rewrite32.0ms (1.1%)

series21.0ms (0.7%)

simplify87.0ms (3.1%)

prune166.0ms (5.9%)

localize30.0ms (1.1%)

rewrite31.0ms (1.1%)

series21.0ms (0.8%)

simplify89.0ms (3.1%)

prune195.0ms (6.9%)

localize18.0ms (0.6%)

rewrite34.0ms (1.2%)

series77.0ms (2.7%)

simplify82.0ms (2.9%)

prune184.0ms (6.5%)

localize19.0ms (0.7%)

rewrite33.0ms (1.2%)

series67.0ms (2.4%)

simplify48.0ms (1.7%)

prune113.0ms (4%)

regimes45.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (42.8%)

Profiling