Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample73.0ms (0.7%)

Algorithm

1×

intervals

Results

53.0ms	256×	body	128	valid
3.0ms	258×	pre	128	true
0.0ms	2×	body	128	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify170.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5512	47

prune9.0ms (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

2.4b

Counts

2 → 2

Compiler

Compiled 163 to 111 computations (31.9% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
2.4b	(exp.f64 (*.f64 x x))

rewrite174.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.8b

Rules

26×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805`
22×	`add-cube-cbrt_binary64_1818` `times-frac_binary64_1789`
15×	`sqrt-prod_binary64_1799`
11×	`add-cbrt-cube_binary64_1819`
10×	`add-exp-log_binary64_1821`
7×	`associate-/l_binary64_1728` `associate-/r_binary64_1727`
6×	`add-log-exp_binary64_1822`
5×	`pow1_binary64_1844`
3×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
2×	`frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `distribute-lft-out_binary64_1734` `associate-/l/_binary64_1730`
1×	`exp-to-pow_binary64_1845` `exp-prod_binary64_1835` `rem-exp-log_binary64_1823` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `flip3-+_binary64_1786` `flip-+_binary64_1757`

Counts

4 → 87

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
5.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
2.0ms	(exp.f64 (*.f64 x x))
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3306 to 1533 computations (53.6% saved)

series202.0ms (2%)

Error

2.3b

Counts

4 → 18

Calls

4 calls:

82.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
66.0ms	(/.f64 (exp.f64 (*.f64 x x)) (sqrt.f64 PI.f64))
25.0ms	(exp.f64 (*.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1434 to 1055 computations (26.4% saved)

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4936	1714
1	4936	1714

prune199.0ms (2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	91	14	105
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Error

0.8b

Counts

107 → 15

Compiler

Compiled 4364 to 2184 computations (50% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
0.4b	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite280.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

46×	`times-frac_binary64_1789`
44×	`*-un-lft-identity_binary64_1783`
41×	`add-sqr-sqrt_binary64_1805`
40×	`add-cube-cbrt_binary64_1818`
27×	`sqrt-prod_binary64_1799`
24×	`unpow-prod-down_binary64_1862`
13×	`add-exp-log_binary64_1821`
11×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728`
8×	`sqr-pow_binary64_1755`
7×	`associate-/r*_binary64_1727`
6×	`pow1_binary64_1844`
5×	`div-exp_binary64_1834`
4×	`pow-pow_binary64_1855` `add-log-exp_binary64_1822`
3×	`pow-unpow_binary64_1860` `exp-prod_binary64_1835` `cbrt-undiv_binary64_1817`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `distribute-lft-out_binary64_1734` `associate-/l/_binary64_1730`
1×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `flip3-+_binary64_1786` `flip-+_binary64_1757`

Counts

4 → 127

Calls

4 calls:

10.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
6.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
4.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 4918 to 2284 computations (53.6% saved)

series230.0ms (2.3%)

Error

0.8b

Counts

4 → 18

Calls

4 calls:

84.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (sqrt.f64 PI.f64))
77.0ms	(/.f64 (+.f64 1/2 (/.f64 3/4 (.f64 x x))) (.f64 x x))
41.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1434 to 1032 computations (28% saved)

simplify111.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4915	2621
1	4915	2621

prune299.0ms (3%)

Pruning

23 alts after pruning (23 fresh and 0 done)

	Pruned	Kept	Total
New	125	20	145
Fresh	11	3	14
Picked	1	0	1
Done	0	0	0
Total	137	23	160

Error

0.3b

Counts

160 → 23

Compiler

Compiled 6293 to 3130 computations (50.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 x) x) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite161.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

15×	`add-sqr-sqrt_binary64_1805` `add-exp-log_binary64_1821`
13×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`unpow-prod-down_binary64_1862` `add-cbrt-cube_binary64_1819`
7×	`pow1_binary64_1844` `times-frac_binary64_1789` `associate-/l*_binary64_1728`
6×	`sqrt-prod_binary64_1799` `div-exp_binary64_1834`
4×	`pow-pow_binary64_1855` `add-log-exp_binary64_1822`
3×	`pow-unpow_binary64_1860` `exp-prod_binary64_1835` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `sqr-pow_binary64_1755` `prod-exp_binary64_1832`
2×	`pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796` `cbrt-undiv_binary64_1817`
1×	`cbrt-unprod_binary64_1816` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-/r*_binary64_1727`

Counts

4 → 79

Calls

4 calls:

13.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3227 to 1398 computations (56.7% saved)

series142.0ms (1.4%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (pow.f64 (exp.f64 x) x) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
42.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1054 to 717 computations (32% saved)

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4953	1091
1	4953	1091

prune184.0ms (1.9%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	87	4	91
Fresh	3	19	22
Picked	0	1	1
Done	0	0	0
Total	90	24	114

Error

0.3b

Counts

114 → 24

Compiler

Compiled 4446 to 2252 computations (49.3% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 x) x)
1.0b	(pow.f64 (exp.f64 x) x)

rewrite127.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

14×	`add-sqr-sqrt_binary64_1805`
12×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
8×	`pow1_binary64_1844` `pow-pow_binary64_1855`
6×	`unpow-prod-down_binary64_1862` `pow-unpow_binary64_1860` `exp-prod_binary64_1835` `sqrt-prod_binary64_1799`
4×	`add-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `sqr-pow_binary64_1755` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`

Counts

4 → 66

Calls

4 calls:

4.0ms	(pow.f64 (exp.f64 x) x)
3.0ms	(pow.f64 (exp.f64 x) x)
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 3072 to 1228 computations (60% saved)

series104.0ms (1%)

Error

0.3b

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow.f64 (exp.f64 x) x)
41.0ms	(pow.f64 (exp.f64 x) x)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1248 to 737 computations (40.9% saved)

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5200	632

prune132.0ms (1.3%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	3	19	22
Picked	0	1	1
Done	0	1	1
Total	77	25	102

Error

0.3b

Counts

102 → 25

Compiler

Compiled 3554 to 1419 computations (60.1% saved)

regimes1.1s (11.5%)

Accuracy

Total 0.9b remaining (75.2%)

Threshold costs 0.9b (75.2%)

Compiler

Compiled 16391 to 10665 computations (34.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	50
1	30	50

end0.0ms (0%)

sample5.8s (58.8%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	128	valid
98.0ms	8127×	pre	128	true
24.0ms	127×	body	128	invalid

Compiler

Compiled 5531 to 3603 computations (34.9% saved)

Details

analyze9.0ms (0.1%)

sample73.0ms (0.7%)

simplify170.0ms (1.7%)

prune9.0ms (0.1%)

localize23.0ms (0.2%)

rewrite174.0ms (1.8%)

series202.0ms (2%)

simplify92.0ms (0.9%)

prune199.0ms (2%)

localize22.0ms (0.2%)

rewrite280.0ms (2.8%)

series230.0ms (2.3%)

simplify111.0ms (1.1%)

prune299.0ms (3%)

localize27.0ms (0.3%)

rewrite161.0ms (1.6%)

series142.0ms (1.4%)

simplify104.0ms (1%)

prune184.0ms (1.9%)

localize27.0ms (0.3%)

rewrite127.0ms (1.3%)

series104.0ms (1%)

simplify51.0ms (0.5%)

prune132.0ms (1.3%)

regimes1.1s (11.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.8s (58.8%)

Profiling