Details

analyze887.0ms (5.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample70.0ms (0.4%)

Algorithm

1×

intervals

Results

27.0ms	119×	body	1024	valid
22.0ms	41×	body	2048	valid
6.0ms	36×	body	512	valid
2.0ms	42×	body	128	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune7.0ms (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

38.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

1.7b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.1b	(tan.f64 (+.f64 x eps))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

20.5b

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`tan-quot_binary64_1942` `add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`tan-sum_binary64_1918` `pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `frac-sub_binary64_1792`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735`

Counts

2 → 27

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 416 to 108 computations (74% saved)

series475.0ms (2.8%)

Error

15.5b

Counts

2 → 23

Calls

2 calls:

278.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
157.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1585 to 928 computations (41.5% saved)

simplify36.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5755	1398

prune63.0ms (0.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	3	51

Error

0.3b

Counts

51 → 3

Compiler

Compiled 1092 to 403 computations (63.1% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite153.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

28×	`*-un-lft-identity_binary64_1783`
23×	`add-sqr-sqrt_binary64_1805`
16×	`add-cube-cbrt_binary64_1818`
13×	`times-frac_binary64_1789`
9×	`tan-quot_binary64_1942`
8×	`add-log-exp_binary64_1822` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`pow1_binary64_1844`
5×	`distribute-lft-out_binary64_1734`
4×	`associate-/l*_binary64_1728`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `associate-r_binary64_1723` `associate-/l/_binary64_1730` `associate-/r*_binary64_1727`
2×	`flip3--_binary64_1787` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-/r/_binary64_1729`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `sub-neg_binary64_1776` `distribute-lft-out--_binary64_1735` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `frac-times_binary64_1793` `unswap-sqr_binary64_1751` `associate-l/_binary64_1726` `associate-r/_binary64_1725` `*-commutative_binary64_1714` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `sum-log_binary64_1874` `+-commutative_binary64_1713`

Counts

4 → 88

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
11.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2365 to 732 computations (69% saved)

series1.9s (11%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

879.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
501.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
234.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
197.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3359 to 1818 computations (45.9% saved)

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5224	3847

prune173.0ms (1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	118	13	131
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	119	15	134

Error

0.1b

Counts

134 → 15

Compiler

Compiled 3936 to 1390 computations (64.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))))
0.2b	(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
0.2b	(*.f64 (sin.f64 eps) (tan.f64 x))
2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))) (tan.f64 x))

rewrite186.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

52×	`*-un-lft-identity_binary64_1783`
43×	`add-sqr-sqrt_binary64_1805`
28×	`times-frac_binary64_1789`
21×	`add-cube-cbrt_binary64_1818`
13×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
12×	`difference-of-squares_binary64_1752`
9×	`associate-/r*_binary64_1727`
7×	`distribute-lft-out_binary64_1734`
6×	`add-log-exp_binary64_1822` `pow1_binary64_1844` `distribute-lft-out--_binary64_1735`
5×	`tan-quot_binary64_1942` `associate-/l*_binary64_1728`
4×	`associate-/l/_binary64_1730`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `associate-r_binary64_1723` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
2×	`flip3--_binary64_1787` `flip--_binary64_1758` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-*r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-/r/_binary64_1729`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `sub-neg_binary64_1776` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757`

Counts

4 → 110

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))) (tan.f64 x))
15.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))))
6.0ms	(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
6.0ms	(*.f64 (sin.f64 eps) (tan.f64 x))

Compiler

Compiled 3439 to 942 computations (72.6% saved)

series1.9s (11.3%)

Error

0.1b

Counts

4 → 41

Calls

4 calls:

913.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))) (tan.f64 x))
517.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))))
254.0ms	(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
170.0ms	(*.f64 (sin.f64 eps) (tan.f64 x))

Compiler

Compiled 3397 to 1837 computations (45.9% saved)

simplify109.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4971	4957
1	4971	4957

prune176.0ms (1%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	151	15	166

Error

0.1b

Counts

166 → 15

Compiler

Compiled 4904 to 1568 computations (68% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (cos.f64 eps) 2)
0.3b	(pow.f64 (sin.f64 eps) 2)
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
2.5b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 eps) 2) (.f64 (tan.f64 x) (tan.f64 x))) (pow.f64 (cos.f64 eps) 2)))) (+.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))) (tan.f64 x))

rewrite194.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_1805`
13×	`pow1_binary64_1844` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`tan-quot_binary64_1942`
8×	`add-exp-log_binary64_1821`
6×	`add-log-exp_binary64_1822` `add-cbrt-cube_binary64_1819` `unpow-prod-down_binary64_1862` `pow-unpow_binary64_1860`
5×	`frac-sub_binary64_1792`
3×	`frac-times_binary64_1793` `associate-r/_binary64_1725` `cancel-sign-sub-inv_binary64_1749` `swap-sqr_binary64_1750` `associate-l_binary64_1724` `associate-r*_binary64_1723`
2×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `associate-*l/_binary64_1726` `associate--l+_binary64_1720` `pow-pow_binary64_1855` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `unpow2_binary64_1848` `sqr-pow_binary64_1755`
1×	`diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `pow2_binary64_1864` `pow-prod-down_binary64_1854` `pow-prod-up_binary64_1853` `pow-plus_binary64_1846` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `pow-sqr_binary64_1756` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`

Counts

4 → 85

Calls

4 calls:

21.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 eps) 2) (.f64 (tan.f64 x) (tan.f64 x))) (pow.f64 (cos.f64 eps) 2)))) (+.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (sin.f64 eps) 2)
2.0ms	(pow.f64 (cos.f64 eps) 2)

Compiler

Compiled 4234 to 1599 computations (62.2% saved)

series3.6s (21.3%)

Error

0.1b

Counts

4 → 22

Calls

4 calls:

3.4s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (pow.f64 (sin.f64 eps) 2) (.f64 (tan.f64 x) (tan.f64 x))) (pow.f64 (cos.f64 eps) 2)))) (+.f64 1 (/.f64 (.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps)))) (tan.f64 x))
55.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
31.0ms	(pow.f64 (sin.f64 eps) 2)
28.0ms	(pow.f64 (cos.f64 eps) 2)

Compiler

Compiled 3466 to 2054 computations (40.7% saved)

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5213	3476

prune186.0ms (1.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	3	10	13
Picked	0	1	1
Done	0	1	1
Total	107	15	122

Error

0.1b

Counts

122 → 15

Compiler

Compiled 5047 to 2030 computations (59.8% saved)

regimes1.3s (7.6%)

Accuracy

Total 0.3b remaining (71.7%)

Threshold costs 0.3b (71.7%)

Compiler

Compiled 13556 to 7735 computations (42.9% saved)

bsearch86.0ms (0.5%)

Steps

Iters	Range		Point
8	4.2108544143077834e-13	4.5052963115667545e-10	4.4594438784481946e-10
9	-5.919770396726862e-07	-3.273192360764738e-12	-3.5166055757565563e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	161
1	130	161

end0.0ms (0%)

sample5.2s (30.9%)

Algorithm

1×

intervals

Results

849.0ms	3491×	body	1024	valid
570.0ms	1220×	body	2048	valid
204.0ms	1334×	body	512	valid
70.0ms	632×	body	256	valid
64.0ms	1323×	body	128	valid

Compiler

Compiled 4613 to 2633 computations (42.9% saved)

Details

analyze887.0ms (5.2%)

sample70.0ms (0.4%)

simplify10.0ms (0.1%)

prune7.0ms (0%)

localize7.0ms (0%)

rewrite39.0ms (0.2%)

series475.0ms (2.8%)

simplify36.0ms (0.2%)

prune63.0ms (0.4%)

localize11.0ms (0.1%)

rewrite153.0ms (0.9%)

series1.9s (11%)

simplify63.0ms (0.4%)

prune173.0ms (1%)

localize15.0ms (0.1%)

rewrite186.0ms (1.1%)

series1.9s (11.3%)

simplify109.0ms (0.6%)

prune176.0ms (1%)

localize23.0ms (0.1%)

rewrite194.0ms (1.1%)

series3.6s (21.3%)

simplify61.0ms (0.4%)

prune186.0ms (1.1%)

regimes1.3s (7.6%)

bsearch86.0ms (0.5%)

simplify5.0ms (0%)

end0.0ms (0%)

sample5.2s (30.9%)

Profiling