Details

analyze77.0ms (2.6%)

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
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	18.7%	12.6%	7
68.7%	12.5%	18.8%	8
68.7%	12.5%	18.8%	9
68.7%	9.4%	22%	10
68.7%	9.4%	22%	11
68.7%	7.8%	23.5%	12
68.7%	7.8%	23.5%	13
68.7%	7%	24.3%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample16.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
1.0ms	21×	body	128	overflowed

Compiler

Compiled 17 to 15 computations (11.8% saved)

simplify93.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	13
1	8	13

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

Error

0.8b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
0.7b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_1783`
12×	`times-frac_binary64_1789`
11×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
5×	`distribute-lft-out_binary64_1734`
4×	`add-cbrt-cube_binary64_1819` `associate-/r*_binary64_1727` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `add-exp-log_binary64_1821`
2×	`associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1_binary64_1844`
1×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782`

Counts

2 → 45

Calls

4 calls:

7.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
0.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
0.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series208.0ms (7%)

Counts

2 → 21

Calls

2 calls:

169.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
38.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

Compiler

Compiled 590 to 444 computations (24.7% saved)

simplify71.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5281	1227

prune55.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	2	67

Error

Counts

67 → 2

Compiler

Compiled 1003 to 292 computations (70.9% saved)

localize11.0ms (0.4%)

Local error

Found 8 expressions with local error:

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

rewrite105.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1783`
88×	`times-frac_binary64_1789`
61×	`add-sqr-sqrt_binary64_1805`
49×	`add-cube-cbrt_binary64_1818`
33×	`unpow-prod-down_binary64_1862`
31×	`cancel-sign-sub-inv_binary64_1749`
23×	`distribute-lft-out_binary64_1734`
14×	`add-exp-log_binary64_1821`
13×	`unpow2_binary64_1848` `associate-/r*_binary64_1727`
11×	`distribute-lft-out--_binary64_1735`
9×	`sqr-pow_binary64_1755` `div-inv_binary64_1780` `add-log-exp_binary64_1822`
8×	`add-cbrt-cube_binary64_1819`
6×	`associate-/l*_binary64_1728` `pow1_binary64_1844`
5×	`difference-of-squares_binary64_1752` `div-exp_binary64_1834`
4×	`distribute-rgt-out_binary64_1736`
3×	`pow-unpow_binary64_1860` `frac-sub_binary64_1792`
2×	`associate-/r/_binary64_1729` `flip-+_binary64_1757` `diff-log_binary64_1875` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `flip3-+_binary64_1786` `clear-num_binary64_1782` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`flip3--_binary64_1787` `inv-pow_binary64_1868` `frac-add_binary64_1791` `1-exp_binary64_1827` `pow-flip_binary64_1857` `sum-log_binary64_1874` `pow-pow_binary64_1855` `associate--l+_binary64_1720` `flip--_binary64_1758` `sub-neg_binary64_1776` `rec-exp_binary64_1833`

Counts

4 → 172

Calls

8 calls:

57.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 (exp.f64 b) 1)) (/.f64 a (+.f64 (exp.f64 b) 1))) (/.f64 a (pow.f64 (+.f64 (exp.f64 b) 1) 2)))
12.0ms	(/.f64 a (pow.f64 (+.f64 (exp.f64 b) 1) 2))
6.0ms	(/.f64 1 (+.f64 (exp.f64 b) 1))
6.0ms	(pow.f64 (+.f64 (exp.f64 b) 1) 2)
0.0ms	(/.f64 a (pow.f64 (+.f64 (exp.f64 b) 1) 2))

series532.0ms (17.8%)

Counts

4 → 27

Calls

4 calls:

319.0ms	(-.f64 (+.f64 (/.f64 1 (+.f64 (exp.f64 b) 1)) (/.f64 a (+.f64 (exp.f64 b) 1))) (/.f64 a (pow.f64 (+.f64 (exp.f64 b) 1) 2)))
154.0ms	(/.f64 a (pow.f64 (+.f64 (exp.f64 b) 1) 2))
30.0ms	(/.f64 1 (+.f64 (exp.f64 b) 1))
29.0ms	(pow.f64 (+.f64 (exp.f64 b) 1) 2)

Compiler

Compiled 973 to 764 computations (21.5% saved)

simplify96.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5061	3900

prune281.0ms (9.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	199	2	201

Error

Counts

201 → 2

Compiler

Compiled 5294 to 3449 computations (34.9% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (exp.f64 a) 1)
0.0b	(+.f64 (exp.f64 a) 1)
0.0b	(/.f64 b (+.f64 (exp.f64 a) 1))
0.0b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) 1))
0.0b	(+.f64 (exp.f64 a) 1)
0.0b	(+.f64 (exp.f64 a) 1)
0.0b	(/.f64 b (+.f64 (exp.f64 a) 1))
0.0b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) 1))

rewrite29.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_1783`
24×	`times-frac_binary64_1789`
22×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818`
10×	`distribute-lft-out_binary64_1734`
8×	`add-cbrt-cube_binary64_1819` `associate-/r*_binary64_1727` `add-log-exp_binary64_1822`
7×	`add-exp-log_binary64_1821`
6×	`associate-/l*_binary64_1728`
4×	`associate-/r/_binary64_1729` `flip-+_binary64_1757` `flip3-+_binary64_1786` `pow1_binary64_1844`
2×	`+-commutative_binary64_1713` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `clear-num_binary64_1782`

Counts

4 → 90

Calls

8 calls:

7.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) 1))
6.0ms	(/.f64 b (+.f64 (exp.f64 a) 1))
4.0ms	(+.f64 (exp.f64 a) 1)
4.0ms	(+.f64 (exp.f64 a) 1)
0.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) 1))

series143.0ms (4.8%)

Counts

4 → 18

Calls

4 calls:

78.0ms	(/.f64 b (+.f64 (exp.f64 a) 1))
37.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) 1))
16.0ms	(+.f64 (exp.f64 a) 1)
11.0ms	(+.f64 (exp.f64 a) 1)

Compiler

Compiled 565 to 449 computations (20.5% saved)

simplify83.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4999	1447
1	4999	1447

prune109.0ms (3.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	108	2	110

Error

Counts

110 → 2

Compiler

Compiled 2374 to 1430 computations (39.8% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	127
1	74	127

regimes64.0ms (2.1%)

Compiler: Compiled 352 to 336 computations (4.5% saved)

bsearch0.0ms (0%)

regimes71.0ms (2.4%)

Compiler: Compiled 124 to 160 computations (-29% saved)

bsearch11.0ms (0.4%)

Steps

Iters	Range		Point
6	-15716.67873490627	-1945.3667569794889	-2277.436057145762

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes45.0ms (1.5%)

Compiler: Compiled 34 to 52 computations (-52.9% saved)

bsearch27.0ms (0.9%)

Steps

Iters	Range		Point
7	5.660262855083375e-20	1.5707465168723226e-18	1.3930900108874062e-18
9	-8.389018791603619e-07	-5.004637633776935e-15	-8.261657521506199e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes40.0ms (1.3%)

Compiler: Compiled 20 to 38 computations (-90% saved)

bsearch29.0ms (1%)

Steps

Iters	Range		Point
7	5.660262855083375e-20	1.5707465168723226e-18	6.941599052022013e-19
9	-8.389018791603619e-07	-5.004637633776935e-15	-8.261657521506199e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes40.0ms (1.4%)

Accuracy

Total 0.8b remaining (99.5%)

Threshold costs 0.8b (99.5%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch15.0ms (0.5%)

Steps

Iters	Range		Point
6	-3734311467.3772116	-363777051.12790394	-370873287.4583278

Compiler

Compiled 59 to 58 computations (1.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	83
1	50	83

end0.0ms (0%)

sample690.0ms (23.1%)

Algorithm

1×

intervals

Results

232.0ms	8000×	body	128	valid
15.0ms	658×	body	128	overflowed

Compiler

Compiled 160 to 152 computations (5% saved)

Pareto

0.8711297449820824

Details

analyze77.0ms (2.6%)

sample16.0ms (0.5%)

simplify93.0ms (3.1%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite14.0ms (0.5%)

series208.0ms (7%)

simplify71.0ms (2.4%)

prune55.0ms (1.9%)

localize11.0ms (0.4%)

rewrite105.0ms (3.5%)

series532.0ms (17.8%)

simplify96.0ms (3.2%)

prune281.0ms (9.4%)

localize9.0ms (0.3%)

rewrite29.0ms (1%)

series143.0ms (4.8%)

simplify83.0ms (2.8%)

prune109.0ms (3.6%)

simplify5.0ms (0.2%)

regimes64.0ms (2.1%)

bsearch0.0ms (0%)

regimes71.0ms (2.4%)

bsearch11.0ms (0.4%)

regimes45.0ms (1.5%)

bsearch27.0ms (0.9%)

regimes40.0ms (1.3%)

bsearch29.0ms (1%)

regimes40.0ms (1.4%)

bsearch15.0ms (0.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample690.0ms (23.1%)

Profiling