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)

sample36.0ms (0.9%)

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)

simplify213.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (119.0ms)

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

Merged error: 0.1b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize18.0ms (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)))
0.3b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite42.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2146`
30×	`associate-r_binary64_2064`
23×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
20×	`times-frac_binary64_2130`
19×	`add-exp-log_binary64_2162`
16×	`add-cbrt-cube_binary64_2160`
13×	`sqrt-prod_binary64_2140`
12×	`pow1_binary64_2185`
9×	`associate-l_binary64_2065`
8×	`prod-exp_binary64_2173`
7×	`unswap-sqr_binary64_2092`
6×	`cbrt-unprod_binary64_2157`
4×	`pow-prod-down_binary64_2195` `unpow-prod-down_binary64_2203` `add-log-exp_binary64_2163`
3×	`*-commutative_binary64_2055`
2×	`sqr-pow_binary64_2096`
1×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193` `associate-*r/_binary64_2066` `div-inv_binary64_2121` `div-exp_binary64_2175`

Counts

4 → 99

Calls

4 calls:

18.0ms	(.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 1/5 (pow.f64 x 4))
6.0ms	(.f64 2/3 (.f64 x x))
2.0ms	(sqrt.f64 PI.f64)

series116.0ms (3%)

Counts

4 → 10

Calls

4 calls:

77.0ms	(.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)))
23.0ms	(*.f64 1/5 (pow.f64 x 4))
16.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5588	2543

prune202.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	5	111

Merged error: 0b

Counts

111 → 5

Compiler

Compiled 3914 to 2630 computations (32.8% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 4) 1/5)
0.1b	(.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))))) (/.f64 1 (sqrt.f64 PI.f64)))
0.3b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite45.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64_2162`
29×	`add-sqr-sqrt_binary64_2146`
26×	`associate-r_binary64_2064`
23×	`add-cbrt-cube_binary64_2160`
22×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
18×	`prod-exp_binary64_2173` `times-frac_binary64_2130`
15×	`pow1_binary64_2185`
12×	`sqrt-prod_binary64_2140`
11×	`associate-l_binary64_2065`
10×	`cbrt-unprod_binary64_2157`
6×	`pow-prod-down_binary64_2195`
5×	`associate-*r/_binary64_2066`
4×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203` `add-log-exp_binary64_2163` `div-exp_binary64_2175`
3×	`*-commutative_binary64_2055`
2×	`cbrt-undiv_binary64_2158` `associate-*l/_binary64_2067` `sqr-pow_binary64_2096` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`un-div-inv_binary64_2122` `sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193` `div-inv_binary64_2121`

Counts

4 → 108

Calls

4 calls:

20.0ms	(.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))))) (/.f64 1 (sqrt.f64 PI.f64)))
6.0ms	(.f64 2/3 (.f64 x x))
5.0ms	(*.f64 (pow.f64 x 4) 1/5)
1.0ms	(sqrt.f64 PI.f64)

series116.0ms (3%)

Counts

4 → 10

Calls

4 calls:

72.0ms	(.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))))) (/.f64 1 (sqrt.f64 PI.f64)))
27.0ms	(*.f64 (pow.f64 x 4) 1/5)
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify81.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4987	2889
1	4987	2889

prune197.0ms (5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	118	5	123

Merged error: 0b

Counts

123 → 5

Compiler

Compiled 3988 to 2707 computations (32.1% saved)

localize22.0ms (0.6%)

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

rewrite38.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
17×	`add-sqr-sqrt_binary64_2146`
13×	`pow1_binary64_2185`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
8×	`associate-r_binary64_2064`
7×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
6×	`sqrt-prod_binary64_2140` `associate-l_binary64_2065`
4×	`pow-prod-down_binary64_2195` `add-log-exp_binary64_2163` `times-frac_binary64_2130`
3×	`unswap-sqr_binary64_2092`
2×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `*-commutative_binary64_2055` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `div-exp_binary64_2175`
1×	`associate-*r/_binary64_2066` `div-inv_binary64_2121`

Counts

4 → 73

Calls

4 calls:

21.0ms	(.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)

series88.0ms (2.3%)

Counts

4 → 8

Calls

4 calls:

71.0ms	(.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)))))
17.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4975	1713
1	4975	1713

prune135.0ms (3.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	81	5	86

Merged error: 0b

Counts

86 → 5

Compiler

Compiled 2933 to 1809 computations (38.3% saved)

localize21.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64))) (/.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 (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)

rewrite52.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64_2146`
55×	`times-frac_binary64_2130`
40×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
31×	`associate-r_binary64_2064`
22×	`sqrt-prod_binary64_2140`
18×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
17×	`cbrt-prod_binary64_2155`
13×	`associate-l_binary64_2065`
8×	`unswap-sqr_binary64_2092`
6×	`pow1_binary64_2185`
5×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
4×	`add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068` `div-inv_binary64_2121`
2×	`pow1/3_binary64_2206`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `associate-l/_binary64_2067` `associate-*r/_binary64_2066` `frac-times_binary64_2134` `frac-2neg_binary64_2135`

Counts

4 → 121

Calls

4 calls:

30.0ms	(.f64 (/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64))) (/.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 (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)

series154.0ms (3.9%)

Counts

4 → 8

Calls

4 calls:

126.0ms	(.f64 (/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64))) (/.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 (cbrt.f64 PI.f64))))
28.0ms	(/.f64 (fabs.f64 x) (fabs.f64 (cbrt.f64 PI.f64)))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

simplify75.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6155	5146

prune255.0ms (6.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	129	5	134

Merged error: 0b

Counts

134 → 5

Compiler

Compiled 5651 to 3170 computations (43.9% saved)

regimes266.0ms (6.8%)

Compiler: Compiled 3571 to 2555 computations (28.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms (0%)

sample1.6s (40.2%)

Algorithm

1×

intervals

Results

794.0ms	8000×	body	128	valid
97.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 712 to 520 computations (27% saved)

Details

analyze6.0ms (0.1%)

sample36.0ms (0.9%)

simplify213.0ms (5.4%)

prune6.0ms (0.2%)

localize18.0ms (0.5%)

rewrite42.0ms (1.1%)

series116.0ms (3%)

simplify72.0ms (1.8%)

prune202.0ms (5.2%)

localize19.0ms (0.5%)

rewrite45.0ms (1.1%)

series116.0ms (3%)

simplify81.0ms (2.1%)

prune197.0ms (5%)

localize22.0ms (0.6%)

rewrite38.0ms (1%)

series88.0ms (2.3%)

simplify67.0ms (1.7%)

prune135.0ms (3.4%)

localize21.0ms (0.5%)

rewrite52.0ms (1.3%)

series154.0ms (3.9%)

simplify75.0ms (1.9%)

prune255.0ms (6.5%)

regimes266.0ms (6.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (40.2%)

Profiling