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 (0.8%)

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)

simplify266.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4911	41
1	4911	41

prune7.0ms (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 (0.4%)

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)

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_1811`
30×	`associate-r_binary64_1729`
23×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
20×	`times-frac_binary64_1795`
19×	`add-exp-log_binary64_1827`
16×	`add-cbrt-cube_binary64_1825`
13×	`sqrt-prod_binary64_1805`
12×	`pow1_binary64_1850`
9×	`associate-l_binary64_1730`
8×	`prod-exp_binary64_1838`
7×	`unswap-sqr_binary64_1757`
6×	`cbrt-unprod_binary64_1822`
4×	`pow-prod-down_binary64_1860` `unpow-prod-down_binary64_1868` `add-log-exp_binary64_1828`
3×	`*-commutative_binary64_1720`
2×	`sqr-pow_binary64_1761`
1×	`associate-*r/_binary64_1731` `cbrt-undiv_binary64_1823` `div-inv_binary64_1786` `pow-exp_binary64_1857` `rem-sqrt-square_binary64_1802` `div-exp_binary64_1840` `sqrt-pow1_binary64_1807` `pow-to-exp_binary64_1858` `pow1/2_binary64_1869`

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)))
7.0ms	(*.f64 1/5 (pow.f64 x 4))
7.0ms	(.f64 2/3 (.f64 x x))
2.0ms	(sqrt.f64 PI.f64)

series222.0ms (5.3%)

Counts

4 → 10

Calls

4 calls:

137.0ms	(.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)))
48.0ms	(*.f64 1/5 (pow.f64 x 4))
38.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5488	2543

prune216.0ms (5.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	106	5	111

Merged error: 0b

Counts

111 → 5

Compiler

Compiled 3972 to 2653 computations (33.2% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

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)))
0.1b	(*.f64 (pow.f64 x 4) 1/5)
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite55.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-exp-log_binary64_1827`
29×	`add-sqr-sqrt_binary64_1811`
26×	`associate-r_binary64_1729`
23×	`add-cbrt-cube_binary64_1825`
22×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
18×	`prod-exp_binary64_1838` `times-frac_binary64_1795`
15×	`pow1_binary64_1850`
12×	`sqrt-prod_binary64_1805`
11×	`associate-l_binary64_1730`
10×	`cbrt-unprod_binary64_1822`
6×	`pow-prod-down_binary64_1860`
5×	`associate-*r/_binary64_1731`
4×	`unpow-prod-down_binary64_1868` `div-exp_binary64_1840` `unswap-sqr_binary64_1757` `add-log-exp_binary64_1828`
3×	`*-commutative_binary64_1720`
2×	`frac-times_binary64_1799` `cbrt-undiv_binary64_1823` `1-exp_binary64_1833` `sqr-pow_binary64_1761` `flip3-+_binary64_1792` `rec-exp_binary64_1839` `flip-+_binary64_1763` `associate-*l/_binary64_1732`
1×	`un-div-inv_binary64_1787` `div-inv_binary64_1786` `pow-exp_binary64_1857` `rem-sqrt-square_binary64_1802` `sqrt-pow1_binary64_1807` `pow-to-exp_binary64_1858` `pow1/2_binary64_1869`

Counts

4 → 108

Calls

4 calls:

24.0ms	(.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)))
10.0ms	(.f64 2/3 (.f64 x x))
7.0ms	(*.f64 (pow.f64 x 4) 1/5)
2.0ms	(sqrt.f64 PI.f64)

series244.0ms (5.9%)

Counts

4 → 10

Calls

4 calls:

152.0ms	(.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)))
57.0ms	(*.f64 (pow.f64 x 4) 1/5)
35.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify96.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4940	2889
1	4940	2889

prune206.0ms (4.9%)

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 4046 to 2730 computations (32.5% saved)

localize30.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (*.f64 (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)

rewrite100.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64_1827`
80×	`pow1_binary64_1850`
79×	`add-cbrt-cube_binary64_1825`
78×	`prod-exp_binary64_1838`
48×	`cbrt-unprod_binary64_1822`
27×	`associate-l_binary64_1730` `pow-prod-down_binary64_1860`
21×	`pow-plus_binary64_1852` `pow-prod-up_binary64_1859` `add-sqr-sqrt_binary64_1811`
20×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
18×	`times-frac_binary64_1795`
13×	`div-exp_binary64_1840`
8×	`cbrt-undiv_binary64_1823`
5×	`1-exp_binary64_1833` `associate-r_binary64_1729` `rec-exp_binary64_1839`
4×	`pow2_binary64_1870` `pow-sqr_binary64_1762` `add-log-exp_binary64_1828`
3×	`*-commutative_binary64_1720` `sqrt-prod_binary64_1805`
2×	`div-inv_binary64_1786` `pow3_binary64_1872` `associate-*l/_binary64_1732`
1×	`rem-sqrt-square_binary64_1802` `sqrt-pow1_binary64_1807` `pow1/2_binary64_1869`

Counts

4 → 148

Calls

4 calls:

33.0ms	(.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)))
11.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)

series238.0ms (5.7%)

Counts

4 → 10

Calls

4 calls:

101.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
81.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
56.0ms	(.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify104.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4903	1421
1	4903	1421

prune409.0ms (9.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	158	5	163

Merged error: 0b

Counts

163 → 5

Compiler

Compiled 9927 to 4029 computations (59.4% 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))
0.3b	(/.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))))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1811`
19×	`add-exp-log_binary64_1827`
16×	`add-cbrt-cube_binary64_1825`
13×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
10×	`associate-l_binary64_1730` `pow1_binary64_1850`
9×	`sqrt-prod_binary64_1805`
7×	`prod-exp_binary64_1838`
6×	`associate-/r*_binary64_1733` `times-frac_binary64_1795`
5×	`cbrt-unprod_binary64_1822`
4×	`associate-r_binary64_1729` `unpow-prod-down_binary64_1868` `unswap-sqr_binary64_1757` `add-log-exp_binary64_1828`
3×	`pow-prod-down_binary64_1860`
2×	`associate-r/_binary64_1731` `cbrt-undiv_binary64_1823` `sqr-pow_binary64_1761` `-commutative_binary64_1720` `associate-/l/_binary64_1736` `div-exp_binary64_1840`
1×	`associate-/l*_binary64_1734` `clear-num_binary64_1788` `div-inv_binary64_1786` `pow-exp_binary64_1857` `rem-sqrt-square_binary64_1802` `frac-2neg_binary64_1800` `sqrt-pow1_binary64_1807` `flip3-+_binary64_1792` `pow-to-exp_binary64_1858` `flip-+_binary64_1763` `pow1/2_binary64_1869`

Counts

4 → 86

Calls

4 calls:

18.0ms	(/.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))))) (sqrt.f64 PI.f64))
7.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 4) 1/5)
2.0ms	(sqrt.f64 PI.f64)

series229.0ms (5.5%)

Counts

4 → 10

Calls

4 calls:

142.0ms	(/.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))))) (sqrt.f64 PI.f64))
50.0ms	(*.f64 (pow.f64 x 4) 1/5)
36.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

simplify51.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	6452	1912

prune156.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	0	1
Picked	0	1	1
Done	1	2	3
Total	97	4	101

Merged error: 0b

Counts

101 → 4

Compiler

Compiled 2957 to 1966 computations (33.5% saved)

regimes115.0ms (2.8%)

Compiler: Compiled 1144 to 673 computations (41.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms (0%)

sample1.2s (27.8%)

Algorithm

1×

intervals

Results

745.0ms	8000×	body	128	valid
100.0ms	8001×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 246 to 155 computations (37% saved)

Details

analyze6.0ms (0.1%)

sample35.0ms (0.8%)

simplify266.0ms (6.4%)

prune7.0ms (0.2%)

localize18.0ms (0.4%)

rewrite53.0ms (1.3%)

series222.0ms (5.3%)

simplify70.0ms (1.7%)

prune216.0ms (5.2%)

localize20.0ms (0.5%)

rewrite55.0ms (1.3%)

series244.0ms (5.9%)

simplify96.0ms (2.3%)

prune206.0ms (4.9%)

localize30.0ms (0.7%)

rewrite100.0ms (2.4%)

series238.0ms (5.7%)

simplify104.0ms (2.5%)

prune409.0ms (9.8%)

localize19.0ms (0.4%)

rewrite42.0ms (1%)

series229.0ms (5.5%)

simplify51.0ms (1.2%)

prune156.0ms (3.7%)

regimes115.0ms (2.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (27.8%)

Profiling