Details

analyze182.0ms (2.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13
0	1	1
1	1	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 (1.4%)

Algorithm

1×

intervals

Results

67.0ms	133×	body	2048	valid
14.0ms	68×	body	1024	valid
4.0ms	27×	body	512	valid
1.0ms	14×	body	256	valid
1.0ms	14×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (87.0ms)

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

Error

28.1b

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)
3.9b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite16.0ms (0.2%)

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)

series35.0ms (0.5%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
7.0ms	(-.f64 (exp.f64 x) 2)

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4887	654
1	4887	654

prune55.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	39	6	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	6	46

Error

0.1b

Counts

46 → 6

Compiler

Compiled 710 to 389 computations (45.2% saved)

localize9.0ms (0.1%)

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

rewrite30.0ms (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:

8.0ms	(+.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))
6.0ms	(*.f64 1/360 (pow.f64 x 6))
5.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))

series161.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
32.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
28.0ms	(*.f64 1/360 (pow.f64 x 6))
23.0ms	(*.f64 1/12 (pow.f64 x 4))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5006	1259

prune99.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	85	7	92

Error

0.1b

Counts

92 → 7

Compiler

Compiled 1877 to 1322 computations (29.6% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
0.0b	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
0.1b	(pow.f64 (exp.f64 x) -3)
3.8b	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))

rewrite61.0ms (0.9%)

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:

19.0ms	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
16.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
6.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)
3.0ms	(pow.f64 (exp.f64 x) -3)

series222.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(+.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) (pow.f64 (exp.f64 x) -3))
34.0ms	(pow.f64 (exp.f64 x) -3)
33.0ms	(*.f64 (-.f64 (exp.f64 x) 2) (-.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x))))
28.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 3)

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4924	2951
1	4924	2951

prune258.0ms (3.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	131	8	139

Error

0.1b

Counts

139 → 8

Compiler

Compiled 5245 to 3149 computations (40% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(pow.f64 (exp.f64 x) -3)
0.1b	(pow.f64 (-.f64 (exp.f64 x) 2) 6)
0.1b	(pow.f64 (exp.f64 x) -6)
3.7b	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 x) -3) 3))

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_1783`
15×	`unpow-prod-down_binary64_1862`
14×	`add-sqr-sqrt_binary64_1805`
12×	`add-cube-cbrt_binary64_1818`
9×	`pow-unpow_binary64_1860` `pow-pow_binary64_1855`
7×	`pow1_binary64_1844`
6×	`exp-prod_binary64_1835` `add-log-exp_binary64_1822`
5×	`add-exp-log_binary64_1821` `distribute-lft-out_binary64_1734`
4×	`add-cbrt-cube_binary64_1819` `cube-prod_binary64_1811`
3×	`sqr-pow_binary64_1755` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`difference-of-squares_binary64_1752` `+-commutative_binary64_1713` `sum-cubes_binary64_1784` `flip-+_binary64_1757` `distribute-lft-out--_binary64_1735` `sum-log_binary64_1874` `flip3-+_binary64_1786`

Counts

4 → 76

Calls

4 calls:

53.0ms	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 x) -3) 3))
5.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 6)
4.0ms	(pow.f64 (exp.f64 x) -6)
3.0ms	(pow.f64 (exp.f64 x) -3)

series833.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

704.0ms	(+.f64 (pow.f64 (pow.f64 (-.f64 (exp.f64 x) 2) 3) 3) (pow.f64 (pow.f64 (exp.f64 x) -3) 3))
51.0ms	(pow.f64 (exp.f64 x) -6)
44.0ms	(pow.f64 (-.f64 (exp.f64 x) 2) 6)
34.0ms	(pow.f64 (exp.f64 x) -3)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4923	1431
1	4923	1431

prune287.0ms (4.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	88	8	96

Error

0.1b

Counts

96 → 8

Compiler

Compiled 5629 to 3663 computations (34.9% saved)

regimes124.0ms (1.9%)

Accuracy

Total 0.6b remaining (97.9%)

Threshold costs 0.6b (97.9%)

Compiler

Compiled 1788 to 1282 computations (28.3% 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%)

sample3.6s (54.9%)

Algorithm

1×

intervals

Results

2.1s	4250×	body	2048	valid
406.0ms	1935×	body	1024	valid
113.0ms	1019×	body	512	valid
32.0ms	441×	body	256	valid
13.0ms	355×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 917 to 662 computations (27.8% saved)

Details

analyze182.0ms (2.8%)

sample93.0ms (1.4%)

simplify93.0ms (1.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite16.0ms (0.2%)

series35.0ms (0.5%)

simplify56.0ms (0.9%)

prune55.0ms (0.8%)

localize9.0ms (0.1%)

rewrite30.0ms (0.5%)

series161.0ms (2.4%)

simplify81.0ms (1.2%)

prune99.0ms (1.5%)

localize15.0ms (0.2%)

rewrite61.0ms (0.9%)

series222.0ms (3.4%)

simplify82.0ms (1.2%)

prune258.0ms (3.9%)

localize26.0ms (0.4%)

rewrite77.0ms (1.2%)

series833.0ms (12.7%)

simplify62.0ms (0.9%)

prune287.0ms (4.4%)

regimes124.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.6s (54.9%)

Profiling