Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample100.0ms (1.7%)

Algorithm

1×

intervals

Results

78.0ms	141×	body	2048	valid
9.0ms	46×	body	1024	valid
5.0ms	42×	body	512	valid
1.0ms	18×	body	256	valid
0.0ms	9×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify170.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13

prune2.0ms (0%)

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: 27.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
5.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1783`
9×	`add-log-exp_binary64_1822`
6×	`add-sqr-sqrt_binary64_1805` `cancel-sign-sub-inv_binary64_1749`
4×	`add-cube-cbrt_binary64_1818` `frac-add_binary64_1791` `associate-+l+_binary64_1716`
3×	`flip3--_binary64_1787` `flip--_binary64_1758`
2×	`add-cbrt-cube_binary64_1819` `exp-diff_binary64_1831` `add-exp-log_binary64_1821` `distribute-lft-out_binary64_1734` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `exp-neg_binary64_1830` `sum-log_binary64_1874` `neg-sub0_binary64_1778` `sub-neg_binary64_1776` `pow1_binary64_1844`
1×	`difference-of-squares_binary64_1752` `+-commutative_binary64_1713` `flip-+_binary64_1757` `associate-+l-_binary64_1718` `flip3-+_binary64_1786`

Counts

2 → 39

Calls

2 calls:

9.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series39.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
8.0ms	(-.f64 (exp.f64 x) 2)

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4887	654
1	4887	654

prune52.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	42	3	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	3	46

Merged error: 0.0b

Counts

46 → 3

Compiler

Compiled 657 to 348 computations (47% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_1805`
14×	`add-exp-log_binary64_1821` `associate-r_binary64_1723`
11×	`add-log-exp_binary64_1822`
10×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
8×	`add-cbrt-cube_binary64_1819` `unpow-prod-down_binary64_1862`
6×	`prod-exp_binary64_1832` `associate-l_binary64_1724` `unswap-sqr_binary64_1751`
4×	`sqr-pow_binary64_1755` `sum-log_binary64_1874` `pow1_binary64_1844`
2×	`+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `flip-+_binary64_1757` `*-commutative_binary64_1714` `flip3-+_binary64_1786` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`associate-+r+_binary64_1715`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
6.0ms	(*.f64 1/12 (pow.f64 x 4))
5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series178.0ms (3%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
34.0ms	(*.f64 1/360 (pow.f64 x 6))
32.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
25.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5006	1259

prune97.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0.0b

Counts

89 → 4

Compiler

Compiled 1834 to 1293 computations (29.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
0.0b	(pow.f64 (exp.f64 x) -3)
4.5b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_1783`
26×	`add-sqr-sqrt_binary64_1805`
17×	`flip3--_binary64_1787` `flip--_binary64_1758`
16×	`add-cube-cbrt_binary64_1818`
12×	`cancel-sign-sub-inv_binary64_1749` `frac-sub_binary64_1792` `frac-times_binary64_1793`
8×	`distribute-lft-in_binary64_1732` `unpow-prod-down_binary64_1862` `distribute-rgt-in_binary64_1733` `associate--l+_binary64_1720` `pow1_binary64_1844`
7×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
6×	`exp-diff_binary64_1831` `associate-r/_binary64_1725` `pow-unpow_binary64_1860` `distribute-lft-out--_binary64_1735` `exp-neg_binary64_1830` `neg-sub0_binary64_1778` `add-log-exp_binary64_1822` `associate-r*_binary64_1723`
5×	`associate-l_binary64_1724` `pow-pow_binary64_1855` `cube-prod_binary64_1811`
4×	`difference-of-squares_binary64_1752` `sub-neg_binary64_1776`
3×	`exp-prod_binary64_1835`
2×	`sqr-pow_binary64_1755` `associate-*l/_binary64_1726` `cube-div_binary64_1812` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`+-commutative_binary64_1713` `rem-cube-cbrt_binary64_1806` `cube-mult_binary64_1813` `distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `unpow3_binary64_1849` `*-commutative_binary64_1714` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751`

Counts

4 → 120

Calls

4 calls:

20.0ms	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
14.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
5.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
3.0ms	(pow.f64 (exp.f64 x) -3)

series238.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
47.0ms	(pow.f64 (exp.f64 x) -3)
31.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
31.0ms	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4924	2951
1	4924	2951

prune245.0ms (4.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

Compiler

Compiled 5141 to 3077 computations (40.1% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) -3)
1.0b	(.f64 (+.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2)) (.f64 (-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
1.6b	(-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2))
4.5b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite91.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`frac-times_binary64_1793`
49×	`flip3--_binary64_1787` `flip--_binary64_1758`
38×	`associate-*r/_binary64_1725`
36×	`frac-sub_binary64_1792`
32×	`distribute-lft-in_binary64_1732` `distribute-rgt-in_binary64_1733`
30×	`cancel-sign-sub-inv_binary64_1749`
28×	`*-un-lft-identity_binary64_1783`
26×	`add-sqr-sqrt_binary64_1805`
22×	`flip-+_binary64_1757` `flip3-+_binary64_1786`
18×	`exp-diff_binary64_1831` `add-cube-cbrt_binary64_1818` `exp-neg_binary64_1830` `neg-sub0_binary64_1778`
16×	`associate--l+_binary64_1720`
11×	`sqrt-prod_binary64_1799`
10×	`pow1_binary64_1844`
9×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `sub-neg_binary64_1776`
8×	`associate-*l/_binary64_1726` `add-log-exp_binary64_1822`
5×	`associate-l_binary64_1724`
4×	`difference-of-squares_binary64_1752` `pow-pow_binary64_1855`
3×	`distribute-lft-out_binary64_1734` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `pow-unpow_binary64_1860` `unpow-prod-down_binary64_1862` `pow-prod-down_binary64_1854` `exp-prod_binary64_1835`
2×	`distribute-lft-out--_binary64_1735`
1×	`+-commutative_binary64_1713` `sqr-pow_binary64_1755` `diff-log_binary64_1875` `-commutative_binary64_1714` `sum-log_binary64_1874` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `associate-r*_binary64_1723`

Counts

4 → 169

Calls

4 calls:

31.0ms	(.f64 (+.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2)) (.f64 (-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
18.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
7.0ms	(-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2))
3.0ms	(pow.f64 (exp.f64 x) -3)

series288.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
93.0ms	(.f64 (+.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2)) (.f64 (-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2)) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))))
36.0ms	(pow.f64 (exp.f64 x) -3)
25.0ms	(-.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 2))

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5000	6847

prune516.0ms (8.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	181	4	185

Merged error: 0b

Counts

185 → 4

Compiler

Compiled 9168 to 5470 computations (40.3% saved)

regimes78.0ms (1.3%)

Compiler: Compiled 942 to 698 computations (25.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.3s (56.3%)

Algorithm

1×

intervals

Results

2.1s	4177×	body	2048	valid
428.0ms	1966×	body	1024	valid
119.0ms	1031×	body	512	valid
33.0ms	482×	body	256	valid
13.0ms	344×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 494 to 370 computations (25.1% saved)

Details

analyze4.0ms (0.1%)

sample100.0ms (1.7%)

simplify170.0ms (2.9%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series39.0ms (0.7%)

simplify54.0ms (0.9%)

prune52.0ms (0.9%)

localize9.0ms (0.2%)

rewrite29.0ms (0.5%)

series178.0ms (3%)

simplify75.0ms (1.3%)

prune97.0ms (1.7%)

localize15.0ms (0.3%)

rewrite56.0ms (1%)

series238.0ms (4.1%)

simplify80.0ms (1.4%)

prune245.0ms (4.2%)

localize21.0ms (0.4%)

rewrite91.0ms (1.6%)

series288.0ms (4.9%)

simplify104.0ms (1.8%)

prune516.0ms (8.8%)

regimes78.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (56.3%)

Profiling