Details

analyze220.0ms (4.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5050	41
0	1	1
1	1	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)

sample38.0ms (0.8%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify126.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5050	41

prune6.0ms (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

0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize18.0ms (0.4%)

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)

rewrite47.0ms (1%)

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:

22.0ms	(.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)))
6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
1.0ms	(sqrt.f64 PI.f64)

series105.0ms (2.2%)

Counts

4 → 10

Calls

4 calls:

64.0ms	(.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)

simplify81.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5588	2543

prune218.0ms (4.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Error

Counts

111 → 4

Compiler

Compiled 3978 to 2654 computations (33.3% saved)

localize31.0ms (0.6%)

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 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (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)

rewrite141.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

177×	`add-exp-log_binary64_2844`
127×	`prod-exp_binary64_2855`
110×	`add-cbrt-cube_binary64_2842`
71×	`cbrt-unprod_binary64_2839`
68×	`pow1_binary64_2867`
37×	`pow-prod-down_binary64_2877`
27×	`associate-l_binary64_2747`
22×	`add-sqr-sqrt_binary64_2828`
20×	`*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812`
17×	`div-exp_binary64_2857`
10×	`cbrt-undiv_binary64_2840`
7×	`1-exp_binary64_2850` `rec-exp_binary64_2856`
6×	`pow-prod-up_binary64_2876` `pow-plus_binary64_2869`
5×	`associate-r_binary64_2746`
4×	`add-log-exp_binary64_2845`
3×	`*-commutative_binary64_2737` `sqrt-prod_binary64_2822`
2×	`pow-sqr_binary64_2779` `div-inv_binary64_2803` `pow2_binary64_2887` `associate-*l/_binary64_2749`
1×	`pow1/2_binary64_2886` `rem-3cbrt-lft_binary64_2831` `pow3_binary64_2889` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `unswap-sqr_binary64_2774`

Counts

4 → 152

Calls

4 calls:

85.0ms	(.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
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))
2.0ms	(sqrt.f64 PI.f64)

series144.0ms (3%)

Counts

4 → 10

Calls

4 calls:

76.0ms	(.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
40.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
27.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4906	1618
1	4906	1618

prune414.0ms (8.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	162	4	166

Error

Counts

166 → 4

Compiler

Compiled 9853 to 4146 computations (57.9% saved)

localize19.0ms (0.4%)

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

rewrite41.0ms (0.8%)

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×	`associate-/l/_binary64_2753` `times-frac_binary64_2812` `associate-/r_binary64_2750` `associate-r/_binary64_2748`
5×	`cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `flip3-+_binary64_2809`
4×	`unpow-prod-down_binary64_2885` `add-log-exp_binary64_2845` `frac-add_binary64_2814` `associate-r_binary64_2746` `unswap-sqr_binary64_2774`
3×	`pow-prod-down_binary64_2877`
2×	`div-exp_binary64_2857` `*-commutative_binary64_2737` `cbrt-undiv_binary64_2840` `sqr-pow_binary64_2778`
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` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817`

Counts

4 → 90

Calls

4 calls:

15.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (+.f64 2 (.f64 2/3 (.f64 x x))) (+.f64 (.f64 (pow.f64 x 6) 1/21) (*.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64))
9.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 4) 1/5)
2.0ms	(sqrt.f64 PI.f64)

series116.0ms (2.4%)

Counts

4 → 10

Calls

4 calls:

71.0ms	(/.f64 (.f64 (fabs.f64 x) (+.f64 (+.f64 2 (.f64 2/3 (.f64 x x))) (+.f64 (.f64 (pow.f64 x 6) 1/21) (*.f64 (pow.f64 x 4) 1/5)))) (sqrt.f64 PI.f64))
24.0ms	(*.f64 (pow.f64 x 4) 1/5)
20.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4972	2104
1	4972	2104

prune176.0ms (3.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	100	4	104

Error

Counts

104 → 4

Compiler

Compiled 3480 to 2359 computations (32.2% saved)

localize25.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 2/3 (.f64 x x))
0.3b	(.f64 (/.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 PI.f64)) (sqrt.f64 (fabs.f64 x)))
0.3b	(.f64 (sqrt.f64 (fabs.f64 x)) (.f64 (/.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 PI.f64)) (sqrt.f64 (fabs.f64 x))))
1.0b	(sqrt.f64 PI.f64)

rewrite63.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_2828`
31×	`associate-l_binary64_2747`
23×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `sqrt-prod_binary64_2822`
22×	`times-frac_binary64_2812`
17×	`pow1_binary64_2867`
10×	`prod-exp_binary64_2855` `cbrt-unprod_binary64_2839`
8×	`associate-r_binary64_2746`
7×	`pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`
4×	`add-log-exp_binary64_2845`
3×	`*-commutative_binary64_2737`
2×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-*l/_binary64_2749`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-*r/_binary64_2748`

Counts

4 → 104

Calls

4 calls:

21.0ms	(.f64 (/.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 PI.f64)) (sqrt.f64 (fabs.f64 x)))
21.0ms	(.f64 (sqrt.f64 (fabs.f64 x)) (.f64 (/.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 PI.f64)) (sqrt.f64 (fabs.f64 x))))
6.0ms	(.f64 2/3 (.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

series148.0ms (3%)

Counts

4 → 10

Calls

4 calls:

70.0ms	(.f64 (sqrt.f64 (fabs.f64 x)) (.f64 (/.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 PI.f64)) (sqrt.f64 (fabs.f64 x))))
61.0ms	(.f64 (/.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 PI.f64)) (sqrt.f64 (fabs.f64 x)))
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4953	3866
1	4953	3866

prune224.0ms (4.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	114	4	118

Error

Counts

118 → 4

Compiler

Compiled 4582 to 2813 computations (38.6% saved)

regimes354.0ms (7.3%)

Accuracy

Total 0.1b remaining (99.8%)

Threshold costs 0.1b (99.8%)

Compiler

Compiled 4760 to 3505 computations (26.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	65
1	34	65

end0.0ms (0%)

sample1.8s (37.8%)

Algorithm

1×

intervals

Results

816.0ms	8000×	body	128	valid
104.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 960 to 715 computations (25.5% saved)

Details

analyze220.0ms (4.5%)

sample38.0ms (0.8%)

simplify126.0ms (2.6%)

prune6.0ms (0.1%)

localize18.0ms (0.4%)

rewrite47.0ms (1%)

series105.0ms (2.2%)

simplify81.0ms (1.7%)

prune218.0ms (4.5%)

localize31.0ms (0.6%)

rewrite141.0ms (2.9%)

series144.0ms (3%)

simplify96.0ms (2%)

prune414.0ms (8.5%)

localize19.0ms (0.4%)

rewrite41.0ms (0.8%)

series116.0ms (2.4%)

simplify73.0ms (1.5%)

prune176.0ms (3.6%)

localize25.0ms (0.5%)

rewrite63.0ms (1.3%)

series148.0ms (3%)

simplify97.0ms (2%)

prune224.0ms (4.6%)

regimes354.0ms (7.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (37.8%)

Profiling