Details

analyze6.0ms (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)

sample35.0ms (1%)

Algorithm

1×

intervals

Results

24.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify221.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

Iter	Nodes	Cost
0	5050	41

prune6.0ms (0.2%)

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

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 x 4))
0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite49.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2828`
30×	`associate-r_binary64_2746`
23×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
20×	`times-frac_binary64_2812`
19×	`add-exp-log_binary64_2844`
16×	`add-cbrt-cube_binary64_2842`
13×	`sqrt-prod_binary64_2822`
12×	`pow1_binary64_2867`
9×	`associate-l_binary64_2747`
8×	`prod-exp_binary64_2855`
7×	`unswap-sqr_binary64_2774`
6×	`cbrt-unprod_binary64_2839`
4×	`unpow-prod-down_binary64_2885` `add-log-exp_binary64_2845` `pow-prod-down_binary64_2877`
3×	`*-commutative_binary64_2737`
2×	`sqr-pow_binary64_2778`
1×	`pow-exp_binary64_2874` `pow1/2_binary64_2886` `div-inv_binary64_2803` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `pow-to-exp_binary64_2875` `rem-sqrt-square_binary64_2819` `associate-*r/_binary64_2748`

Counts

4 → 99

Calls

4 calls:

20.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
7.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
2.0ms	(sqrt.f64 PI.f64)

series109.0ms (3%)

Counts

4 → 10

Calls

4 calls:

68.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
24.0ms	(*.f64 1/5 (pow.f64 x 4))
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify71.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5588	2543

prune208.0ms (5.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	3	111

Error

Counts

111 → 3

Compiler

Compiled 3909 to 2622 computations (32.9% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
17×	`add-sqr-sqrt_binary64_2828`
13×	`pow1_binary64_2867`
10×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
8×	`associate-r_binary64_2746`
7×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
6×	`associate-l_binary64_2747` `sqrt-prod_binary64_2822`
4×	`times-frac_binary64_2812` `add-log-exp_binary64_2845` `pow-prod-down_binary64_2877`
3×	`unswap-sqr_binary64_2774`
2×	`pow1/2_binary64_2886` `div-exp_binary64_2857` `*-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819`
1×	`div-inv_binary64_2803` `associate-*r/_binary64_2748`

Counts

4 → 73

Calls

4 calls:

23.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))
6.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series92.0ms (2.5%)

Counts

4 → 8

Calls

4 calls:

76.0ms	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64)))))
16.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify62.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4975	1713
1	4975	1713

prune135.0ms (3.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

Counts

84 → 3

Compiler

Compiled 2956 to 1825 computations (38.3% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 4) 1/5)
0.2b	(.f64 2/3 (.f64 x x))
0.3b	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite41.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2828`
19×	`add-exp-log_binary64_2844`
16×	`add-cbrt-cube_binary64_2842`
13×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
10×	`associate-l_binary64_2747` `pow1_binary64_2867`
9×	`sqrt-prod_binary64_2822`
7×	`prod-exp_binary64_2855`
6×	`times-frac_binary64_2812` `associate-/r*_binary64_2750`
5×	`cbrt-unprod_binary64_2839`
4×	`unpow-prod-down_binary64_2885` `add-log-exp_binary64_2845` `associate-r_binary64_2746` `unswap-sqr_binary64_2774`
3×	`pow-prod-down_binary64_2877`
2×	`associate-/l/_binary64_2753` `div-exp_binary64_2857` `-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `sqr-pow_binary64_2778` `associate-r/_binary64_2748`
1×	`pow-exp_binary64_2874` `pow1/2_binary64_2886` `div-inv_binary64_2803` `sqrt-pow1_binary64_2824` `pow-to-exp_binary64_2875` `rem-sqrt-square_binary64_2819` `flip-+_binary64_2780` `flip3-+_binary64_2809` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817`

Counts

4 → 86

Calls

4 calls:

18.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 4) 1/5)
1.0ms	(sqrt.f64 PI.f64)

series105.0ms (2.9%)

Counts

4 → 10

Calls

4 calls:

65.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 PI.f64))
24.0ms	(*.f64 (pow.f64 x 4) 1/5)
16.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify56.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6505	1912

prune147.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Error

Counts

99 → 3

Compiler

Compiled 2988 to 1991 computations (33.4% saved)

localize21.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64))) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 (cbrt.f64 PI.f64)))
0.5b	(/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64)))
1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812`
15×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
12×	`associate-/r*_binary64_2750` `sqrt-prod_binary64_2822` `cbrt-prod_binary64_2837`
5×	`associate-/l/_binary64_2753` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
4×	`add-log-exp_binary64_2845` `associate-/l*_binary64_2751` `pow1_binary64_2867`
2×	`frac-times_binary64_2816` `div-inv_binary64_2803` `pow1/3_binary64_2888` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `flip3-+_binary64_2809` `clear-num_binary64_2805` `associate-*r/_binary64_2748` `frac-2neg_binary64_2817`
1×	`associate-*l/_binary64_2749`

Counts

4 → 89

Calls

4 calls:

22.0ms	(/.f64 (.f64 (/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64))) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 (cbrt.f64 PI.f64)))
3.0ms	(/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64)))
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)

series141.0ms (3.8%)

Counts

4 → 8

Calls

4 calls:

116.0ms	(/.f64 (.f64 (/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64))) (+.f64 (.f64 (pow.f64 x 6) 1/21) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 (pow.f64 x 4) 1/5))))) (sqrt.f64 (cbrt.f64 PI.f64)))
25.0ms	(/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64)))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

simplify74.0ms (2%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4965	3056
1	4965	3056

prune167.0ms (4.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	97	3	100

Error

Counts

100 → 3

Compiler

Compiled 3676 to 2053 computations (44.2% saved)

regimes257.0ms (7%)

Accuracy

Total 0.1b remaining (99.1%)

Threshold costs 0.1b (99.1%)

Compiler

Compiled 3421 to 2450 computations (28.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms (0%)

sample1.5s (41.6%)

Algorithm

1×

intervals

Results

772.0ms	8000×	body	128	valid
101.0ms	8003×	pre	128	true
0.0ms	3×	body	128	invalid

Compiler

Compiled 682 to 499 computations (26.8% saved)

Details

analyze6.0ms (0.2%)

sample35.0ms (1%)

simplify221.0ms (6%)

prune6.0ms (0.2%)

localize19.0ms (0.5%)

rewrite49.0ms (1.3%)

series109.0ms (3%)

simplify71.0ms (1.9%)

prune208.0ms (5.7%)

localize20.0ms (0.5%)

rewrite40.0ms (1.1%)

series92.0ms (2.5%)

simplify62.0ms (1.7%)

prune135.0ms (3.7%)

localize18.0ms (0.5%)

rewrite41.0ms (1.1%)

series105.0ms (2.9%)

simplify56.0ms (1.5%)

prune147.0ms (4%)

localize21.0ms (0.6%)

rewrite38.0ms (1%)

series141.0ms (3.8%)

simplify74.0ms (2%)

prune167.0ms (4.5%)

regimes257.0ms (7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.5s (41.6%)

Profiling