Details

analyze882.0ms (7.2%)

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)

sample60.0ms (0.5%)

Algorithm

1×

intervals

Results

25.0ms	109×	body	1024	valid
12.0ms	31×	body	2048	valid
7.0ms	45×	body	512	valid
2.0ms	53×	body	128	valid
2.0ms	18×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune6.0ms (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

36.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.8b	(tan.f64 (+.f64 x eps))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

21.6b

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)

series477.0ms (3.9%)

Error

13.1b

Counts

2 → 22

Calls

2 calls:

271.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
170.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1514 to 887 computations (41.4% saved)

simplify37.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5606	1292

prune57.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.2b

Counts

50 → 3

Compiler

Compiled 1005 to 358 computations (64.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite143.0ms (1.2%)

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` `sum-log_binary64_1874` `+-commutative_binary64_1713` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780`

Counts

4 → 88

Calls

4 calls:

14.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
9.0ms	(/.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))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2365 to 732 computations (69% saved)

series1.9s (15.1%)

Error

0.2b

Counts

4 → 41

Calls

4 calls:

911.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
499.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
201.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
200.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3192 to 1725 computations (46% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5054	3692

prune162.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	117	12	129
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	118	14	132

Error

0.1b

Counts

132 → 14

Compiler

Compiled 3784 to 1304 computations (65.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (sin.f64 eps) (tan.f64 x))
0.2b	(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
3.5b	(-.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))

rewrite118.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

16×	`add-sqr-sqrt_binary64_1805`
13×	`*-un-lft-identity_binary64_1783`
11×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
9×	`add-cube-cbrt_binary64_1818`
8×	`add-log-exp_binary64_1822`
6×	`pow1_binary64_1844`
5×	`tan-quot_binary64_1942`
4×	`times-frac_binary64_1789`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-/r_binary64_1727` `associate-l_binary64_1724` `associate-r*_binary64_1723`
2×	`difference-of-squares_binary64_1752` `prod-exp_binary64_1832` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `cbrt-unprod_binary64_1816` `associate-*r/_binary64_1725`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `distribute-lft-out--_binary64_1735` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-/l/_binary64_1730` `associate-/l_binary64_1728` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `-commutative_binary64_1714` `sum-log_binary64_1874` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out_binary64_1734` `+-commutative_binary64_1713`

Counts

4 → 72

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))
8.0ms	(*.f64 (sin.f64 eps) (tan.f64 x))
6.0ms	(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2025 to 568 computations (72% saved)

series1.5s (12.6%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

921.0ms	(-.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))
228.0ms	(/.f64 (*.f64 (sin.f64 eps) (tan.f64 x)) (cos.f64 eps))
187.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
171.0ms	(*.f64 (sin.f64 eps) (tan.f64 x))

Compiler

Compiled 3007 to 1592 computations (47.1% saved)

simplify69.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4970	2617
1	4970	2617

prune123.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	111	14	125

Error

0.1b

Counts

125 → 14

Compiler

Compiled 3350 to 1075 computations (67.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (sin.f64 eps) (sin.f64 x))
0.2b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
3.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))

rewrite128.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

18×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
14×	`add-sqr-sqrt_binary64_1805`
11×	`*-un-lft-identity_binary64_1783`
8×	`add-log-exp_binary64_1822`
7×	`add-cube-cbrt_binary64_1818`
6×	`pow1_binary64_1844`
5×	`prod-exp_binary64_1832` `cbrt-unprod_binary64_1816`
4×	`div-exp_binary64_1834` `cbrt-undiv_binary64_1817`
3×	`tan-quot_binary64_1942` `cancel-sign-sub-inv_binary64_1749` `associate-l_binary64_1724` `associate-r_binary64_1723`
2×	`difference-of-squares_binary64_1752` `times-frac_binary64_1789` `sin-mult_binary64_1938`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `distribute-lft-out--_binary64_1735` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `associate-/l/_binary64_1730` `cos-mult_binary64_1937` `associate-/r/_binary64_1729` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714` `sum-log_binary64_1874` `frac-add_binary64_1791` `flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-lft-out_binary64_1734` `+-commutative_binary64_1713`

Counts

4 → 73

Calls

4 calls:

21.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
8.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2368 to 588 computations (75.2% saved)

series1.4s (11.5%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

873.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
210.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
184.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
110.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 3067 to 1609 computations (47.5% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5375	2752

prune107.0ms (0.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	112	14	126

Error

0.1b

Counts

126 → 14

Compiler

Compiled 3228 to 861 computations (73.3% saved)

regimes799.0ms (6.5%)

Accuracy

Total 0.6b remaining (79.5%)

Threshold costs 0.6b (79.5%)

Compiler

Compiled 7676 to 4315 computations (43.8% saved)

bsearch67.0ms (0.5%)

Steps

Iters	Range		Point
5	7.3092921016363e-25	1.543020605012958e-24	1.5288277488061028e-24
10	-9.754421942945754	-9.869296060744658e-17	-3.1787671774722826e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	107	127
1	107	127

end0.0ms (0%)

sample4.0s (32.8%)

Algorithm

1×

intervals

Results

811.0ms	3373×	body	1024	valid
590.0ms	1266×	body	2048	valid
210.0ms	1421×	body	512	valid
65.0ms	1335×	body	128	valid
57.0ms	603×	body	256	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 2624 to 1481 computations (43.6% saved)

Details

analyze882.0ms (7.2%)

sample60.0ms (0.5%)

simplify9.0ms (0.1%)

prune6.0ms (0.1%)

localize7.0ms (0.1%)

rewrite39.0ms (0.3%)

series477.0ms (3.9%)

simplify37.0ms (0.3%)

prune57.0ms (0.5%)

localize10.0ms (0.1%)

rewrite143.0ms (1.2%)

series1.9s (15.1%)

simplify59.0ms (0.5%)

prune162.0ms (1.3%)

localize14.0ms (0.1%)

rewrite118.0ms (1%)

series1.5s (12.6%)

simplify69.0ms (0.6%)

prune123.0ms (1%)

localize18.0ms (0.1%)

rewrite128.0ms (1%)

series1.4s (11.5%)

simplify54.0ms (0.4%)

prune107.0ms (0.9%)

regimes799.0ms (6.5%)

bsearch67.0ms (0.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (32.8%)

Profiling