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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify268.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5203	47

prune10.0ms (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)

localize27.0ms (0.4%)

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

rewrite125.0ms (1.8%)

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:

33.0ms	(.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)))))
32.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
14.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series707.0ms (9.9%)

Counts

4 → 10

Calls

4 calls:

530.0ms	(.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)))))
96.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
80.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify121.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5010	5420

prune523.0ms (7.4%)

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 11085 to 5151 computations (53.5% saved)

localize23.0ms (0.3%)

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))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite57.0ms (0.8%)

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:

21.0ms	(.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)))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))

series806.0ms (11.3%)

Counts

4 → 12

Calls

4 calls:

526.0ms	(.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)))
109.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
99.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
72.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5267	3518

prune508.0ms (7.1%)

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 5250 to 3740 computations (28.8% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.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 (sqrt.f64 PI.f64))))
0.3b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.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 (sqrt.f64 PI.f64)))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite81.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`sqrt-prod_binary64_2451`
51×	`add-sqr-sqrt_binary64_2457`
40×	`times-frac_binary64_2442`
37×	`*-un-lft-identity_binary64_2436`
35×	`add-cube-cbrt_binary64_2468`
28×	`associate-l_binary64_2379`
26×	`associate-r_binary64_2378`
15×	`sqrt-div_binary64_2452`
13×	`pow1_binary64_2494`
11×	`add-exp-log_binary64_2471` `add-cbrt-cube_binary64_2469` `frac-times_binary64_2446`
8×	`associate-*r/_binary64_2380`
7×	`associate-*l/_binary64_2381`
6×	`flip3-+_binary64_2439` `flip-+_binary64_2410` `unswap-sqr_binary64_2404`
4×	`prod-exp_binary64_2482` `pow-prod-down_binary64_2504` `add-log-exp_binary64_2472` `cbrt-unprod_binary64_2466`
2×	`*-commutative_binary64_2369` `div-inv_binary64_2433` `pow1/2_binary64_2513` `rem-sqrt-square_binary64_2449` `sqrt-pow1_binary64_2453`

Counts

4 → 127

Calls

4 calls:

32.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.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 (sqrt.f64 PI.f64)))))
24.0ms	(.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 (sqrt.f64 PI.f64))))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series1.2s (17.3%)

Counts

4 → 8

Calls

4 calls:

692.0ms	(.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 (sqrt.f64 PI.f64))))
535.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 PI.f64))) (.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 (sqrt.f64 PI.f64)))))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify109.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4996	6683
1	4996	6683

prune364.0ms (5.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	135	4	139

Merged error: 0b

Counts

139 → 4

Compiler

Compiled 6614 to 4502 computations (31.9% saved)

localize20.0ms (0.3%)

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))

rewrite38.0ms (0.5%)

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)

series360.0ms (5.1%)

Counts

4 → 6

Calls

4 calls:

359.0ms	(/.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)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5009	3173

prune239.0ms (3.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	112	4	116

Merged error: 0b

Counts

116 → 4

Compiler

Compiled 4614 to 2896 computations (37.2% saved)

regimes111.0ms (1.6%)

Compiler: Compiled 1234 to 728 computations (41% 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 (16.4%)

Algorithm

1×

intervals

Results

739.0ms	8000×	body	128	valid
107.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 269 to 169 computations (37.2% saved)

Details

analyze6.0ms (0.1%)

sample39.0ms (0.6%)

simplify268.0ms (3.8%)

prune10.0ms (0.1%)

localize27.0ms (0.4%)

rewrite125.0ms (1.8%)

series707.0ms (9.9%)

simplify121.0ms (1.7%)

prune523.0ms (7.4%)

localize23.0ms (0.3%)

rewrite57.0ms (0.8%)

series806.0ms (11.3%)

simplify90.0ms (1.3%)

prune508.0ms (7.1%)

localize24.0ms (0.3%)

rewrite81.0ms (1.1%)

series1.2s (17.3%)

simplify109.0ms (1.5%)

prune364.0ms (5.1%)

localize20.0ms (0.3%)

rewrite38.0ms (0.5%)

series360.0ms (5.1%)

simplify62.0ms (0.9%)

prune239.0ms (3.4%)

regimes111.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (16.4%)

Profiling