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)

sample93.0ms (1.8%)

Algorithm

1×

intervals

Results

66.0ms	127×	body	2048	valid
14.0ms	65×	body	1024	valid
4.0ms	33×	body	512	valid
1.0ms	18×	body	256	valid
0.0ms	13×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify180.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13

prune3.0ms (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

Error

30.9b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
5.1b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite15.0ms (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:

8.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
4.0ms	(-.f64 (exp.f64 x) 2)

series35.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

27.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
8.0ms	(-.f64 (exp.f64 x) 2)

simplify52.0ms (1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4887	654
1	4887	654

prune49.0ms (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

Error

0.0b

Counts

46 → 3

Compiler

Compiled 636 to 337 computations (47% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.1b	(*.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 1/12 (pow.f64 x 4))
5.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series172.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
35.0ms	(*.f64 1/360 (pow.f64 x 6))
30.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
26.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5006	1259

prune98.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Error

0.0b

Counts

89 → 3

Compiler

Compiled 1764 to 1242 computations (29.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 2 (exp.f64 (neg.f64 x)))
4.9b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_1783`
11×	`add-sqr-sqrt_binary64_1805` `cancel-sign-sub-inv_binary64_1749`
9×	`add-log-exp_binary64_1822`
5×	`add-cube-cbrt_binary64_1818` `distribute-lft-out--_binary64_1735`
4×	`diff-log_binary64_1875` `associate--r+_binary64_1719`
3×	`difference-of-squares_binary64_1752` `sub-neg_binary64_1776`
2×	`flip3--_binary64_1787` `add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `flip--_binary64_1758` `pow1_binary64_1844`
1×	`associate--r-_binary64_1722`

Counts

2 → 41

Calls

2 calls:

8.0ms	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 2 (exp.f64 (neg.f64 x)))

series41.0ms (0.8%)

Counts

2 → 6

Calls

2 calls:

31.0ms	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
9.0ms	(-.f64 2 (exp.f64 (neg.f64 x)))

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4832	659
1	4832	659

prune33.0ms (0.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	46	4	50

Error

0.0b

Counts

50 → 4

Compiler

Compiled 653 to 339 computations (48.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
0.1b	(pow.f64 (exp.f64 x) -3)
0.3b	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) -2) (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
4.3b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite58.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805`
19×	`add-cube-cbrt_binary64_1818`
12×	`times-frac_binary64_1789`
8×	`unpow-prod-down_binary64_1862`
7×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
6×	`pow-unpow_binary64_1860` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`distribute-lft-out_binary64_1734` `pow-pow_binary64_1855` `cube-prod_binary64_1811`
4×	`associate-/l*_binary64_1728`
3×	`flip-+_binary64_1757` `associate-/r*_binary64_1727` `flip3-+_binary64_1786` `exp-prod_binary64_1835`
2×	`associate-/l/_binary64_1730` `associate-/r/_binary64_1729` `difference-of-squares_binary64_1752` `sqr-pow_binary64_1755` `distribute-lft-out--_binary64_1735` `cube-div_binary64_1812` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`flip3--_binary64_1787` `+-commutative_binary64_1713` `rem-cube-cbrt_binary64_1806` `cube-mult_binary64_1813` `unpow3_binary64_1849` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

4 → 96

Calls

4 calls:

20.0ms	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) -2) (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
17.0ms	(+.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)

series704.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(/.f64 (+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3)) (+.f64 (pow.f64 (exp.f64 x) -2) (*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))))
126.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
39.0ms	(pow.f64 (exp.f64 x) -3)
32.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5038	3530

prune202.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	108	4	112

Error

0.0b

Counts

112 → 4

Compiler

Compiled 4355 to 2598 computations (40.3% saved)

regimes45.0ms (0.9%)

Accuracy

Total 0.6b remaining (97%)

Threshold costs 0.6b (97%)

Compiler

Compiled 446 to 338 computations (24.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample3.1s (59.6%)

Algorithm

1×

intervals

Results

2.1s	4124×	body	2048	valid
454.0ms	2027×	body	1024	valid
114.0ms	972×	body	512	valid
36.0ms	510×	body	256	valid
14.0ms	367×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 246 to 190 computations (22.8% saved)

Details

analyze4.0ms (0.1%)

sample93.0ms (1.8%)

simplify180.0ms (3.4%)

prune3.0ms (0%)

localize10.0ms (0.2%)

rewrite15.0ms (0.3%)

series35.0ms (0.7%)

simplify52.0ms (1%)

prune49.0ms (0.9%)

localize9.0ms (0.2%)

rewrite29.0ms (0.5%)

series172.0ms (3.3%)

simplify80.0ms (1.5%)

prune98.0ms (1.9%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series41.0ms (0.8%)

simplify84.0ms (1.6%)

prune33.0ms (0.6%)

localize15.0ms (0.3%)

rewrite58.0ms (1.1%)

series704.0ms (13.4%)

simplify84.0ms (1.6%)

prune202.0ms (3.8%)

regimes45.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.1s (59.6%)

Profiling