Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample27.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms	79×	body	1024	valid
4.0ms	44×	body	512	valid
3.0ms	105×	body	128	valid
1.0ms	23×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify186.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	166	9
1	166	9

prune2.0ms (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: 39.1b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.1b	(-.f64 (exp.f64 x) 1)

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1821`
30×	`*-un-lft-identity_binary64_1799`
21×	`times-frac_binary64_1805`
15×	`add-cube-cbrt_binary64_1834`
10×	`difference-of-squares_binary64_1768`
7×	`associate-/l*_binary64_1744`
5×	`difference-of-sqr-1_binary64_1769` `distribute-lft-out--_binary64_1751`
4×	`add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
3×	`associate-/r*_binary64_1743` `cancel-sign-sub-inv_binary64_1765`
2×	`pow1_binary64_1860` `flip--_binary64_1774` `flip3--_binary64_1803` `associate-/l/_binary64_1746`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `clear-num_binary64_1798` `div-exp_binary64_1850` `frac-2neg_binary64_1810` `diff-log_binary64_1891` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796`

Counts

2 → 64

Calls

2 calls:

8.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
5.0ms	(-.f64 (exp.f64 x) 1)

series74.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

56.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
18.0ms	(-.f64 (exp.f64 x) 1)

simplify110.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4874	1016
1	4874	1016

prune96.0ms (2.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	2	71

Merged error: 0.0b

Counts

71 → 2

Compiler

Compiled 1376 to 861 computations (37.4% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
0.0b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1821`
7×	`pow1_binary64_1860` `add-cube-cbrt_binary64_1834` `add-cbrt-cube_binary64_1835` `*-un-lft-identity_binary64_1799` `add-exp-log_binary64_1837`
6×	`associate-l_binary64_1740` `associate-r_binary64_1739`
5×	`add-log-exp_binary64_1838`
2×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `prod-exp_binary64_1848` `unswap-sqr_binary64_1767` `associate-r/_binary64_1741` `associate-+r+_binary64_1731` `cbrt-unprod_binary64_1832` `-commutative_binary64_1730` `pow-prod-down_binary64_1870` `flip3-+_binary64_1802` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729`

Counts

3 → 53

Calls

3 calls:

6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
6.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))
4.0ms	(*.f64 x 1/6)

series133.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

83.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
28.0ms	(*.f64 x 1/6)
22.0ms	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x 1/6))))

simplify58.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5000	713

prune50.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	62	2	64

Merged error: 0.0b

Counts

64 → 2

Compiler

Compiled 857 to 674 computations (21.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
4.0b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite82.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`times-frac_binary64_1805`
238×	`*-un-lft-identity_binary64_1799`
156×	`add-sqr-sqrt_binary64_1821`
112×	`add-cube-cbrt_binary64_1834`
88×	`difference-of-sqr--1_binary64_1770`
63×	`distribute-lft-out_binary64_1750`
46×	`associate-/l*_binary64_1744`
25×	`unpow-prod-down_binary64_1878`
23×	`unpow2_binary64_1864` `sqr-pow_binary64_1771`
11×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
10×	`associate-/r/_binary64_1745`
7×	`associate-/r*_binary64_1743` `flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`add-log-exp_binary64_1838` `div-inv_binary64_1796`
5×	`pow1_binary64_1860`
4×	`div-exp_binary64_1850` `cbrt-undiv_binary64_1833` `pow-pow_binary64_1871`
3×	`pow-unpow_binary64_1876` `associate-/l/_binary64_1746` `exp-prod_binary64_1851`
2×	`clear-num_binary64_1798` `frac-2neg_binary64_1810`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `pow-to-exp_binary64_1868` `pow-exp_binary64_1867`

Counts

4 → 267

Calls

4 calls:

23.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
14.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
7.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.0ms	(pow.f64 (exp.f64 x) 2)

series323.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(/.f64 (/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1)) x)
108.0ms	(/.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1) (+.f64 (exp.f64 x) 1))
37.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
20.0ms	(pow.f64 (exp.f64 x) 2)

simplify116.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4932	7296
1	4932	7296

prune324.0ms (9.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	278	3	281

Merged error: 0.0b

Counts

281 → 3

Compiler

Compiled 6166 to 3806 computations (38.3% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 2)
0.0b	(pow.f64 (exp.f64 x) 2)
0.2b	(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) 2)) (.f64 -1 -1)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 1) (+.f64 (exp.f64 x) 1)))
4.0b	(-.f64 (.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) 2)) (.f64 -1 -1))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
9×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
8×	`associate-/r/_binary64_1745` `pow-pow_binary64_1871`
6×	`pow1_binary64_1860` `add-log-exp_binary64_1838` `pow-unpow_binary64_1876` `unpow-prod-down_binary64_1878` `exp-prod_binary64_1851` `flip3-+_binary64_1802` `flip-+_binary64_1773`
4×	`associate-/l*_binary64_1744` `times-frac_binary64_1805` `frac-times_binary64_1809`
3×	`difference-of-squares_binary64_1768`
2×	`div-exp_binary64_1850` `unpow2_binary64_1864` `pow-to-exp_binary64_1868` `associate-r/_binary64_1741` `flip--_binary64_1774` `flip3--_binary64_1803` `cbrt-undiv_binary64_1833` `associate-/l/_binary64_1746` `pow-exp_binary64_1867` `sqr-pow_binary64_1771` `associate-l/_binary64_1742`
1×	`div-sub_binary64_1804` `sub-neg_binary64_1792` `clear-num_binary64_1798` `prod-exp_binary64_1848` `frac-2neg_binary64_1810` `associate-/r*_binary64_1743` `diff-log_binary64_1891` `cbrt-unprod_binary64_1832` `div-inv_binary64_1796` `cancel-sign-sub-inv_binary64_1765`

Counts

4 → 89

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) 2)) (.f64 -1 -1)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 1) (+.f64 (exp.f64 x) 1)))
8.0ms	(-.f64 (.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) 2)) (.f64 -1 -1))
4.0ms	(pow.f64 (exp.f64 x) 2)
4.0ms	(pow.f64 (exp.f64 x) 2)

series512.0ms (14.6%)

Counts

4 → 12

Calls

4 calls:

413.0ms	(/.f64 (-.f64 (.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) 2)) (.f64 -1 -1)) (*.f64 (+.f64 (pow.f64 (exp.f64 x) 2) 1) (+.f64 (exp.f64 x) 1)))
58.0ms	(-.f64 (.f64 (pow.f64 (exp.f64 x) 2) (pow.f64 (exp.f64 x) 2)) (.f64 -1 -1))
21.0ms	(pow.f64 (exp.f64 x) 2)
20.0ms	(pow.f64 (exp.f64 x) 2)

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1375
1	4951	1375

prune163.0ms (4.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	101	3	104

Merged error: 0.0b

Counts

104 → 3

Compiler

Compiled 3255 to 2194 computations (32.6% saved)

regimes16.0ms (0.4%)

Compiler: Compiled 58 to 44 computations (24.1% saved)

bsearch18.0ms (0.5%)

Steps

Iters	Range		Point
8	-0.00046930186408040693	-1.756281169177105e-06	-0.00011513130775083037

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	70
1	41	70

end0.0ms (0%)

sample1.0s (29.4%)

Algorithm

1×

intervals

Results

458.0ms	2661×	body	1024	valid
130.0ms	1340×	body	512	valid
87.0ms	3080×	body	128	valid
55.0ms	290×	body	2048	valid
39.0ms	629×	body	256	valid

Compiler

Compiled 130 to 96 computations (26.2% saved)

Details

analyze4.0ms (0.1%)

sample27.0ms (0.8%)

simplify186.0ms (5.3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite18.0ms (0.5%)

series74.0ms (2.1%)

simplify110.0ms (3.1%)

prune96.0ms (2.7%)

localize6.0ms (0.2%)

rewrite19.0ms (0.6%)

series133.0ms (3.8%)

simplify58.0ms (1.6%)

prune50.0ms (1.4%)

localize8.0ms (0.2%)

rewrite82.0ms (2.3%)

series323.0ms (9.2%)

simplify116.0ms (3.3%)

prune324.0ms (9.2%)

localize13.0ms (0.4%)

rewrite51.0ms (1.4%)

series512.0ms (14.6%)

simplify63.0ms (1.8%)

prune163.0ms (4.7%)

regimes16.0ms (0.4%)

bsearch18.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (29.4%)

Profiling