Details

analyze6.0ms (0.1%)

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)

sample38.0ms (0.4%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify270.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	5203	47

prune7.0ms (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: 0.0b

Counts

2 → 2

Compiler

Compiled 125 to 77 computations (38.4% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.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)))))
0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite123.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64_2471`
76×	`prod-exp_binary64_2482`
75×	`add-cbrt-cube_binary64_2469`
48×	`associate-l_binary64_2379`
46×	`add-sqr-sqrt_binary64_2457`
44×	`cbrt-unprod_binary64_2466`
40×	`times-frac_binary64_2442`
36×	`pow1_binary64_2494`
35×	`*-un-lft-identity_binary64_2436`
33×	`add-cube-cbrt_binary64_2468`
22×	`pow-prod-down_binary64_2504`
15×	`div-exp_binary64_2484` `associate-*l/_binary64_2381`
14×	`sqrt-prod_binary64_2451`
12×	`frac-add_binary64_2444`
9×	`cbrt-undiv_binary64_2467`
6×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `rec-exp_binary64_2483` `1-exp_binary64_2477` `associate-*r/_binary64_2380` `frac-times_binary64_2446`
5×	`unswap-sqr_binary64_2404` `associate-r_binary64_2378`
4×	`add-log-exp_binary64_2472`
3×	`*-commutative_binary64_2369` `div-inv_binary64_2433`
1×	`distribute-rgt-in_binary64_2388` `pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `distribute-lft-in_binary64_2387` `sqrt-pow1_binary64_2453`

Counts

4 → 169

Calls

4 calls:

35.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
30.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.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)))
2.0ms	(sqrt.f64 PI.f64)

series750.0ms (7.8%)

Counts

4 → 10

Calls

4 calls:

568.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.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)))))
99.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
82.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5010	5420

prune570.0ms (5.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	176	3	179
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	177	4	181

Merged error: 0b

Counts

181 → 4

Compiler

Compiled 11151 to 5201 computations (53.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64_2457`
42×	`associate-r_binary64_2378`
24×	`*-un-lft-identity_binary64_2436`
23×	`add-cube-cbrt_binary64_2468`
21×	`add-exp-log_binary64_2471`
16×	`sqrt-prod_binary64_2451`
14×	`unswap-sqr_binary64_2404`
12×	`unpow-prod-down_binary64_2512` `add-cbrt-cube_binary64_2469` `associate-l_binary64_2379`
11×	`times-frac_binary64_2442`
10×	`prod-exp_binary64_2482`
6×	`sqr-pow_binary64_2408` `pow1_binary64_2494`
4×	`*-commutative_binary64_2369` `add-log-exp_binary64_2472` `cbrt-unprod_binary64_2466` `cube-prod_binary64_2461`
3×	`pow-to-exp_binary64_2502` `pow-exp_binary64_2501` `sqrt-div_binary64_2452`
2×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `associate-*l/_binary64_2381` `frac-times_binary64_2446`
1×	`div-inv_binary64_2433` `pow-prod-down_binary64_2504` `associate-*r/_binary64_2380` `cube-mult_binary64_2463` `unpow3_binary64_2499`

Counts

4 → 120

Calls

4 calls:

22.0ms	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))

series824.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

541.0ms	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
115.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
96.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
72.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5267	3518

prune298.0ms (3.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0b

Counts

136 → 4

Compiler

Compiled 5316 to 3790 computations (28.7% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2457`
36×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436` `times-frac_binary64_2442`
30×	`sqrt-prod_binary64_2451`
12×	`associate-/r*_binary64_2382`
8×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
6×	`associate-/l*_binary64_2383` `pow1_binary64_2494`
4×	`add-log-exp_binary64_2472`
2×	`cbrt-undiv_binary64_2467` `div-inv_binary64_2433` `pow1/2_binary64_2513` `div-exp_binary64_2484` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `frac-2neg_binary64_2447` `associate-/l/_binary64_2385` `sqrt-pow1_binary64_2453`
1×	`flip3-+_binary64_2439` `flip-+_binary64_2410`

Counts

4 → 106

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
5.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series342.0ms (3.6%)

Counts

4 → 6

Calls

4 calls:

342.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5009	3173

prune249.0ms (2.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	112	4	116

Merged error: 0b

Counts

116 → 4

Compiler

Compiled 4718 to 2976 computations (36.9% saved)

localize45.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 5 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))))
0.3b	(.f64 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105)
1.0b	(sqrt.f64 PI.f64)
39.6b	(/.f64 (+.f64 (.f64 21 (+.f64 (.f64 5 (+.f64 (.f64 8/27 (pow.f64 (fabs.f64 x) 9)) (.f64 (pow.f64 (fabs.f64 x) 3) 8))) (.f64 (pow.f64 (fabs.f64 x) 5) (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (sqrt.f64 PI.f64) (.f64 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105)))

rewrite105.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`associate-*r/_binary64_2380`
20×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `frac-add_binary64_2444`
17×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469`
16×	`add-sqr-sqrt_binary64_2457`
14×	`associate-/l/_binary64_2385`
11×	`add-cube-cbrt_binary64_2468` `*-un-lft-identity_binary64_2436`
9×	`pow1_binary64_2494`
6×	`associate-r_binary64_2378` `associate-l_binary64_2379`
5×	`prod-exp_binary64_2482` `cbrt-unprod_binary64_2466`
4×	`add-log-exp_binary64_2472` `associate-*l/_binary64_2381`
3×	`cbrt-undiv_binary64_2467` `associate-/l*_binary64_2383` `div-exp_binary64_2484` `sqrt-prod_binary64_2451` `times-frac_binary64_2442`
2×	`*-commutative_binary64_2369` `pow-prod-down_binary64_2504` `associate-/r/_binary64_2384` `unswap-sqr_binary64_2404`
1×	`distribute-rgt-in_binary64_2388` `div-inv_binary64_2433` `pow1/2_binary64_2513` `associate-/r*_binary64_2382` `clear-num_binary64_2435` `rem-sqrt-square_binary64_2449` `frac-2neg_binary64_2447` `distribute-lft-in_binary64_2387` `sqrt-pow1_binary64_2453`

Counts

4 → 94

Calls

4 calls:

36.0ms	(/.f64 (+.f64 (.f64 21 (+.f64 (.f64 5 (+.f64 (.f64 8/27 (pow.f64 (fabs.f64 x) 9)) (.f64 (pow.f64 (fabs.f64 x) 3) 8))) (.f64 (pow.f64 (fabs.f64 x) 5) (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (sqrt.f64 PI.f64) (.f64 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105)))
13.0ms	(.f64 5 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))))
12.0ms	(.f64 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105)
1.0ms	(sqrt.f64 PI.f64)

series3.0s (30.9%)

Counts

4 → 10

Calls

4 calls:

2.2s	(/.f64 (+.f64 (.f64 21 (+.f64 (.f64 5 (+.f64 (.f64 8/27 (pow.f64 (fabs.f64 x) 9)) (.f64 (pow.f64 (fabs.f64 x) 3) 8))) (.f64 (pow.f64 (fabs.f64 x) 5) (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (.f64 (pow.f64 (fabs.f64 x) 4) 2/3))))))) (.f64 (sqrt.f64 PI.f64) (.f64 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105)))
370.0ms	(.f64 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))) 105)
362.0ms	(.f64 5 (+.f64 (.f64 (pow.f64 (fabs.f64 x) 2) 4) (-.f64 (.f64 4/9 (pow.f64 (fabs.f64 x) 6)) (.f64 2 (*.f64 (pow.f64 (fabs.f64 x) 4) 2/3)))))
0.0ms	(sqrt.f64 PI.f64)

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5079	9053

prune1.1s (11.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	104	4	108

Merged error: 0b

Counts

108 → 4

Compiler

Compiled 15814 to 11510 computations (27.2% saved)

regimes129.0ms (1.3%)

Compiler: Compiled 1564 to 978 computations (37.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	50
1	35	50

end0.0ms (0%)

sample1.2s (12.5%)

Algorithm

1×

intervals

Results

728.0ms	8000×	body	128	valid
103.0ms	8002×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 335 to 219 computations (34.6% saved)

Details

analyze6.0ms (0.1%)

sample38.0ms (0.4%)

simplify270.0ms (2.8%)

prune7.0ms (0.1%)

localize26.0ms (0.3%)

rewrite123.0ms (1.3%)

series750.0ms (7.8%)

simplify120.0ms (1.3%)

prune570.0ms (5.9%)

localize19.0ms (0.2%)

rewrite57.0ms (0.6%)

series824.0ms (8.6%)

simplify85.0ms (0.9%)

prune298.0ms (3.1%)

localize21.0ms (0.2%)

rewrite34.0ms (0.4%)

series342.0ms (3.6%)

simplify63.0ms (0.7%)

prune249.0ms (2.6%)

localize45.0ms (0.5%)

rewrite105.0ms (1.1%)

series3.0s (30.9%)

simplify110.0ms (1.1%)

prune1.1s (11.9%)

regimes129.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (12.5%)

Profiling