Details

analyze70.0ms (2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample24.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	235×	body	128	valid
3.0ms	5×	body	1024	valid
2.0ms	12×	body	256	valid
1.0ms	4×	body	512	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify172.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	96	14
1	96	14

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: 0.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite18.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1799`
8×	`log-prod_binary64_1885`
6×	`add-log-exp_binary64_1838`
5×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
4×	`pow1_binary64_1860` `associate--l+_binary64_1736` `add-exp-log_binary64_1837` `log-div_binary64_1886`
3×	`add-cbrt-cube_binary64_1835` `distribute-lft-out_binary64_1750` `flip3-+_binary64_1802` `flip-+_binary64_1773`
2×	`associate--l-_binary64_1737`
1×	`sum-log_binary64_1890` `sub-neg_binary64_1792` `+-commutative_binary64_1729` `diff-log_binary64_1891` `flip--_binary64_1774` `flip3--_binary64_1803` `log-pow_binary64_1888` `cancel-sign-sub-inv_binary64_1765` `rem-log-exp_binary64_1840`

Counts

3 → 45

Calls

3 calls:

7.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series161.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

80.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
71.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
10.0ms	(+.f64 1 (exp.f64 x))

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5066	767

prune102.0ms (2.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.5b

Counts

55 → 4

Compiler

Compiled 1524 to 1052 computations (31% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.5b	(log.f64 (+.f64 1 (exp.f64 x)))
0.7b	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
0.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_1799`
14×	`cbrt-prod_binary64_1830`
11×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
10×	`pow1_binary64_1860`
8×	`unpow-prod-down_binary64_1878` `cube-prod_binary64_1827`
6×	`add-log-exp_binary64_1838` `add-exp-log_binary64_1837`
5×	`add-cbrt-cube_binary64_1835` `log-pow_binary64_1888`
4×	`log-prod_binary64_1885`
3×	`pow-unpow_binary64_1876`
2×	`cube-mult_binary64_1829` `unpow3_binary64_1865` `sqr-pow_binary64_1771` `distribute-lft-out_binary64_1750` `flip3-+_binary64_1802` `log-div_binary64_1886` `flip-+_binary64_1773`
1×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `rem-cbrt-cube_binary64_1823` `pow1/3_binary64_1881` `pow-to-exp_binary64_1868` `pow-exp_binary64_1867` `pow-pow_binary64_1871` `rem-cube-cbrt_binary64_1822` `rem-log-exp_binary64_1840`

Counts

4 → 75

Calls

4 calls:

4.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))
3.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
3.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))

series303.0ms (8.7%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3)
85.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 1 (exp.f64 x))) 3))
74.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
9.0ms	(+.f64 1 (exp.f64 x))

simplify92.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4882	1105
1	4882	1105

prune90.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Merged error: 0.4b

Counts

91 → 5

Compiler

Compiled 1527 to 1001 computations (34.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.5b	(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
0.7b	(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite50.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64_1860`
34×	`sqrt-prod_binary64_1815`
32×	`*-un-lft-identity_binary64_1799`
30×	`add-sqr-sqrt_binary64_1821`
28×	`sqrt-div_binary64_1816`
18×	`pow1/2_binary64_1879` `sqrt-pow1_binary64_1817`
14×	`add-cube-cbrt_binary64_1834` `log-pow_binary64_1888` `flip3-+_binary64_1802` `flip-+_binary64_1773`
11×	`swap-sqr_binary64_1766`
10×	`pow-prod-up_binary64_1869`
9×	`add-exp-log_binary64_1837`
8×	`distribute-lft-out_binary64_1750` `log-div_binary64_1886` `frac-times_binary64_1809`
7×	`associate-l_binary64_1740` `associate-r_binary64_1739`
6×	`pow-sqr_binary64_1772` `add-cbrt-cube_binary64_1835` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838` `unswap-sqr_binary64_1767` `associate-r/_binary64_1741` `rem-sqrt-square_binary64_1812` `associate-l/_binary64_1742`
2×	`pow2_binary64_1880` `prod-exp_binary64_1848` `pow-plus_binary64_1862` `rem-log-exp_binary64_1840`
1×	`log-prod_binary64_1885` `sqr-abs_binary64_1814` `cbrt-unprod_binary64_1832` `*-commutative_binary64_1730` `sqrt-unprod_binary64_1819` `rem-square-sqrt_binary64_1811`

Counts

4 → 127

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))
15.0ms	(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series155.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(log.f64 (*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x)))))
37.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
33.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
12.0ms	(*.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (+.f64 1 (exp.f64 x))))

simplify91.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5056	1742

prune150.0ms (4.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	140	4	144

Merged error: 0.4b

Counts

144 → 4

Compiler

Compiled 2749 to 1746 computations (36.5% saved)

localize20.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))))
0.2b	(.f64 (.f64 x x) (+.f64 3/4 (*.f64 3/8 (log.f64 2))))
0.8b	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
9.6b	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))))))

rewrite54.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`associate-*r/_binary64_1741`
15×	`pow1_binary64_1860`
14×	`add-sqr-sqrt_binary64_1821`
13×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
12×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
9×	`add-cube-cbrt_binary64_1834` `associate-l_binary64_1740` `-un-lft-identity_binary64_1799` `associate-r*_binary64_1739`
8×	`frac-add_binary64_1807`
6×	`cbrt-div_binary64_1831`
5×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838`
3×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `unswap-sqr_binary64_1767` `*-commutative_binary64_1730`
2×	`log-pow_binary64_1888`
1×	`pow1/3_binary64_1881` `cbrt-prod_binary64_1830`

Counts

4 → 88

Calls

4 calls:

14.0ms	(.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))))
12.0ms	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))))))
9.0ms	(.f64 (.f64 x x) (+.f64 3/4 (*.f64 3/8 (log.f64 2))))
8.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))

series606.0ms (17.3%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))
203.0ms	(cbrt.f64 (.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2))))))
112.0ms	(.f64 (.f64 x x) (+.f64 3/4 (*.f64 3/8 (log.f64 2))))
71.0ms	(.f64 (log.f64 2) (+.f64 (.f64 (.f64 x x) (+.f64 3/4 (.f64 3/8 (log.f64 2)))) (.f64 (log.f64 2) (+.f64 (log.f64 2) (.f64 x 3/2)))))

simplify91.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5028	3505

prune253.0ms (7.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	100	4	104

Merged error: 0.4b

Counts

104 → 4

Compiler

Compiled 4374 to 3526 computations (19.4% saved)

regimes25.0ms (0.7%)

Compiler: Compiled 174 to 158 computations (9.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	19
1	40	19

end0.0ms (0%)

sample856.0ms (24.4%)

Algorithm

1×

intervals

Results

370.0ms	7388×	body	128	valid
87.0ms	206×	body	1024	valid
54.0ms	236×	body	512	valid
21.0ms	167×	body	256	valid
4.0ms	3×	body	2048	valid
2.0ms	40×	body	128	invalid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 133 to 117 computations (12% saved)

Details

analyze70.0ms (2%)

sample24.0ms (0.7%)

simplify172.0ms (4.9%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite18.0ms (0.5%)

series161.0ms (4.6%)

simplify63.0ms (1.8%)

prune102.0ms (2.9%)

localize10.0ms (0.3%)

rewrite19.0ms (0.5%)

series303.0ms (8.7%)

simplify92.0ms (2.6%)

prune90.0ms (2.6%)

localize10.0ms (0.3%)

rewrite50.0ms (1.4%)

series155.0ms (4.4%)

simplify91.0ms (2.6%)

prune150.0ms (4.3%)

localize20.0ms (0.6%)

rewrite54.0ms (1.5%)

series606.0ms (17.3%)

simplify91.0ms (2.6%)

prune253.0ms (7.2%)

regimes25.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample856.0ms (24.4%)

Profiling