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)

sample35.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify265.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4911	41
1	4911	41

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: 0.1b

Counts

2 → 2

Compiler

Compiled 212 to 128 computations (39.6% saved)

localize26.0ms (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)

rewrite126.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64_2181`
76×	`prod-exp_binary64_2192`
75×	`add-cbrt-cube_binary64_2179`
48×	`associate-l_binary64_2084`
46×	`add-sqr-sqrt_binary64_2165`
44×	`cbrt-unprod_binary64_2176`
40×	`times-frac_binary64_2149`
36×	`pow1_binary64_2204`
35×	`*-un-lft-identity_binary64_2143`
33×	`add-cube-cbrt_binary64_2178`
22×	`pow-prod-down_binary64_2214`
15×	`associate-*l/_binary64_2086` `div-exp_binary64_2194`
14×	`sqrt-prod_binary64_2159`
12×	`frac-add_binary64_2151`
9×	`cbrt-undiv_binary64_2177`
6×	`frac-times_binary64_2153` `1-exp_binary64_2187` `rec-exp_binary64_2193` `associate-*r/_binary64_2085` `flip3-+_binary64_2146` `flip-+_binary64_2117`
5×	`associate-r_binary64_2083` `unswap-sqr_binary64_2111`
4×	`add-log-exp_binary64_2182`
3×	`div-inv_binary64_2140` `*-commutative_binary64_2074`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `distribute-rgt-in_binary64_2093` `sqrt-pow1_binary64_2161` `distribute-lft-in_binary64_2092`

Counts

4 → 169

Calls

4 calls:

31.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
29.0ms	(.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)))))
16.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series937.0ms (13.9%)

Counts

4 → 10

Calls

4 calls:

759.0ms	(.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)))))
107.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
71.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify129.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4911	5273
1	4911	5273

prune731.0ms (10.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	175	4	179
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	4	181

Merged error: 0b

Counts

181 → 4

Compiler

Compiled 15535 to 8092 computations (47.9% 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 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.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 (.f64 x x))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64_2165`
31×	`associate-r_binary64_2083`
21×	`add-exp-log_binary64_2181` `*-un-lft-identity_binary64_2143`
20×	`add-cube-cbrt_binary64_2178`
16×	`sqrt-prod_binary64_2159`
15×	`add-cbrt-cube_binary64_2179`
12×	`associate-l_binary64_2084`
11×	`pow1_binary64_2204` `unswap-sqr_binary64_2111` `times-frac_binary64_2149`
10×	`prod-exp_binary64_2192`
8×	`unpow-prod-down_binary64_2222`
6×	`cbrt-unprod_binary64_2176`
4×	`add-log-exp_binary64_2182` `pow-prod-down_binary64_2214` `sqr-pow_binary64_2115` `*-commutative_binary64_2074`
3×	`sqrt-div_binary64_2160`
2×	`frac-times_binary64_2153` `pow-to-exp_binary64_2212` `associate-*l/_binary64_2086` `flip3-+_binary64_2146` `flip-+_binary64_2117` `pow-exp_binary64_2211`
1×	`div-inv_binary64_2140` `associate-*r/_binary64_2085`

Counts

4 → 108

Calls

4 calls:

17.0ms	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
7.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))

series840.0ms (12.4%)

Counts

4 → 12

Calls

4 calls:

593.0ms	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
118.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
94.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
34.0ms	(.f64 2/3 (.f64 x x))

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4867	3207
1	4867	3207

prune246.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Merged error: 0b

Counts

124 → 4

Compiler

Compiled 4686 to 3180 computations (32.1% saved)

localize28.0ms (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)))) (pow.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) 1)) (.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 1/5 (pow.f64 (fabs.f64 x) 5))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite81.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt_binary64_2165`
39×	`add-exp-log_binary64_2181`
38×	`associate-l_binary64_2084`
32×	`add-cbrt-cube_binary64_2179`
31×	`times-frac_binary64_2149` `*-un-lft-identity_binary64_2143`
29×	`add-cube-cbrt_binary64_2178`
19×	`prod-exp_binary64_2192`
16×	`pow1_binary64_2204`
15×	`cbrt-unprod_binary64_2176`
14×	`sqrt-prod_binary64_2159`
11×	`associate-r_binary64_2083`
8×	`unswap-sqr_binary64_2111`
7×	`pow-prod-down_binary64_2214`
6×	`associate-*l/_binary64_2086`
5×	`div-exp_binary64_2194`
4×	`cbrt-undiv_binary64_2177` `add-log-exp_binary64_2182` `unpow-prod-down_binary64_2222` `frac-times_binary64_2153` `associate-*r/_binary64_2085` `flip3-+_binary64_2146` `flip-+_binary64_2117` `frac-add_binary64_2151`
3×	`*-commutative_binary64_2074`
2×	`div-inv_binary64_2140` `sqr-pow_binary64_2115`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `distribute-rgt-in_binary64_2093` `1-exp_binary64_2187` `pow-to-exp_binary64_2212` `rec-exp_binary64_2193` `sqrt-pow1_binary64_2161` `distribute-lft-in_binary64_2092` `pow-exp_binary64_2211`

Counts

4 → 132

Calls

4 calls:

28.0ms	(.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)))) (pow.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) 1)) (.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)))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
2.0ms	(sqrt.f64 PI.f64)

series711.0ms (10.5%)

Counts

4 → 10

Calls

4 calls:

551.0ms	(.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)))) (pow.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) 1)) (.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)))))
91.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
67.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify120.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4980	4299
1	4980	4299

prune374.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	142	4	146

Merged error: 0b

Counts

146 → 4

Compiler

Compiled 7916 to 4020 computations (49.2% 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 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (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))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_2165`
36×	`add-cube-cbrt_binary64_2178` `times-frac_binary64_2149` `*-un-lft-identity_binary64_2143`
30×	`sqrt-prod_binary64_2159`
12×	`associate-/r*_binary64_2087`
8×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
6×	`pow1_binary64_2204` `associate-/l*_binary64_2088`
4×	`add-log-exp_binary64_2182`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `div-inv_binary64_2140` `sqrt-pow1_binary64_2161` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `associate-/l/_binary64_2090`
1×	`flip3-+_binary64_2146` `flip-+_binary64_2117`

Counts

4 → 106

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (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)

series394.0ms (5.8%)

Counts

4 → 6

Calls

4 calls:

394.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (.f64 (fabs.f64 x) (+.f64 (.f64 2/3 (.f64 x x)) 2))) (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)

simplify107.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4926	3064
1	4926	3064

prune209.0ms (3.1%)

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 4487 to 2628 computations (41.4% saved)

regimes33.0ms (0.5%)

Compiler: Compiled 298 to 210 computations (29.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	48
1	34	48

end0.0ms (0%)

sample1.1s (16.8%)

Algorithm

1×

intervals

Results

741.0ms	8000×	body	128	valid
97.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 246 to 160 computations (35% saved)

Details

analyze6.0ms (0.1%)

sample35.0ms (0.5%)

simplify265.0ms (3.9%)

prune10.0ms (0.1%)

localize26.0ms (0.4%)

rewrite126.0ms (1.9%)

series937.0ms (13.9%)

simplify129.0ms (1.9%)

prune731.0ms (10.8%)

localize23.0ms (0.3%)

rewrite49.0ms (0.7%)

series840.0ms (12.4%)

simplify82.0ms (1.2%)

prune246.0ms (3.6%)

localize28.0ms (0.4%)

rewrite81.0ms (1.2%)

series711.0ms (10.5%)

simplify120.0ms (1.8%)

prune374.0ms (5.5%)

localize20.0ms (0.3%)

rewrite31.0ms (0.5%)

series394.0ms (5.8%)

simplify107.0ms (1.6%)

prune209.0ms (3.1%)

regimes33.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (16.8%)

Profiling