Details

analyze764.0ms (0.6%)

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
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)

sample77.0ms (0.1%)

Algorithm

1×

intervals

Results

33.0ms	115×	body	1024	valid
19.0ms	45×	body	2048	valid
7.0ms	50×	body	512	valid
2.0ms	15×	body	256	valid
1.0ms	31×	body	128	valid

Compiler

Compiled 18 to 20 computations (-11.1% saved)

simplify106.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	14
1	72	14

prune2.0ms (0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Kept	Total
New	4	4
Fresh	4	4
Picked	0	0
Done	0	0
Total	8	8

Error

37.3b

Counts

8 → 4

Compiler

Compiled 10 to 9 computations (10% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

3.6b	(tan.f64 (+.f64 x eps))
0.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
0.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.6b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

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×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `tan-sum_binary64_1918` `frac-sub_binary64_1792` `pow1_binary64_1844`
1×	`flip3--_binary64_1787` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776`

Counts

2 → 27

Calls

4 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
0.0ms	(tan.f64 (+.f64 x eps))

series454.0ms (0.3%)

Counts

2 → 23

Calls

2 calls:

290.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
164.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 904 to 607 computations (32.9% saved)

simplify40.0ms (0%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5755	1398

prune228.0ms (0.2%)

Pruning

40 alts after pruning (39 fresh and 1 done)

	Pruned	Kept	Total
New	14	36	50
Fresh	0	3	3
Picked	0	0	0
Done	0	1	1
Total	14	40	54

Error

0.3b

Counts

54 → 40

Compiler

Compiled 1738 to 894 computations (48.6% saved)

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
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))))
0.1b	(-.f64 1 (*.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))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.3b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

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-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821` `add-log-exp_binary64_1822`
6×	`pow1_binary64_1844`
5×	`distribute-lft-out_binary64_1734`
4×	`associate-/l*_binary64_1728`
3×	`associate-/l/_binary64_1730` `cancel-sign-sub-inv_binary64_1749` `associate-/r_binary64_1727` `associate-l_binary64_1724` `associate-r*_binary64_1723`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `difference-of-squares_binary64_1752` `frac-add_binary64_1791` `flip-+_binary64_1757` `flip3-+_binary64_1786` `flip--_binary64_1758`
1×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `distribute-lft-out--_binary64_1735` `associate-l/_binary64_1726` `diff-log_binary64_1875` `frac-sub_binary64_1792` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `frac-times_binary64_1793` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `sub-neg_binary64_1776`

Counts

4 → 88

Calls

8 calls:

13.0ms	(-.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))))
7.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (1.5%)

Counts

4 → 44

Calls

4 calls:

991.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
553.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
235.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
205.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2034 to 1301 computations (36% saved)

simplify66.0ms (0%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5352	3915

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `times-frac_binary64_1789`
3×	`add-cbrt-cube_binary64_1819` `associate-/l_binary64_1728` `add-exp-log_binary64_1821` `associate-/r_binary64_1727`
1×	`quot-tan_binary64_1943` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `add-log-exp_binary64_1822` `pow1_binary64_1844`

Counts

1 → 28

Calls

2 calls:

4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))

series31.0ms (0%)

Counts

1 → 4

Calls

1 calls:

31.0ms

(/.f64 (sin.f64 eps) (cos.f64 eps))

Compiler

Compiled 41 to 41 computations (0% saved)

simplify122.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5543	426

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

6.0b	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
3.6b	(tan.f64 (+.f64 x eps))
0.7b	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
0.2b	(log.f64 (tan.f64 (+.f64 x eps)))
0.2b	(log.f64 (tan.f64 (+.f64 x eps)))
0.7b	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
3.6b	(tan.f64 (+.f64 x eps))
6.0b	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1805`
10×	`*-un-lft-identity_binary64_1783`
8×	`add-cube-cbrt_binary64_1818`
7×	`log-prod_binary64_1869`
6×	`tan-quot_binary64_1942` `add-log-exp_binary64_1822` `log-div_binary64_1870` `pow1_binary64_1844`
5×	`add-exp-log_binary64_1821`
4×	`add-cbrt-cube_binary64_1819` `exp-diff_binary64_1831` `exp-sum_binary64_1829` `tan-sum_binary64_1918` `exp-prod_binary64_1835`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`difference-of-squares_binary64_1752` `log-pow_binary64_1872` `frac-sub_binary64_1792`
1×	`flip3--_binary64_1787` `rem-exp-log_binary64_1823` `distribute-lft-out--_binary64_1735` `diff-log_binary64_1875` `flip--_binary64_1758` `sub-neg_binary64_1776` `rem-log-exp_binary64_1824`

Counts

4 → 59

Calls

8 calls:

10.0ms	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
6.0ms	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
4.0ms	(log.f64 (tan.f64 (+.f64 x eps)))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(log.f64 (tan.f64 (+.f64 x eps)))

series1.4s (1.1%)

Counts

4 → 45

Calls

4 calls:

520.0ms	(-.f64 (exp.f64 (log.f64 (tan.f64 (+.f64 x eps)))) (tan.f64 x))
403.0ms	(exp.f64 (log.f64 (tan.f64 (+.f64 x eps))))
348.0ms	(log.f64 (tan.f64 (+.f64 x eps)))
153.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 2296 to 1279 computations (44.3% saved)

simplify59.0ms (0%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5144	2642

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (sin.f64 eps) 2)
0.2b	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.0b	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)))
0.2b	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
0.2b	(pow.f64 (sin.f64 eps) 2)
0.3b	(pow.f64 (cos.f64 eps) 2)
3.1b	(*.f64 x (pow.f64 (sin.f64 eps) 2))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-exp-log_binary64_1821`
21×	`add-sqr-sqrt_binary64_1805`
16×	`unpow-prod-down_binary64_1862`
15×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
12×	`prod-exp_binary64_1832` `div-exp_binary64_1834`
11×	`add-cbrt-cube_binary64_1819`
10×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
8×	`associate-/r_binary64_1727` `times-frac_binary64_1789` `associate-r*_binary64_1723`
6×	`sqr-pow_binary64_1755` `pow-unpow_binary64_1860` `unpow2_binary64_1848` `pow1_binary64_1844`
4×	`unswap-sqr_binary64_1751` `add-log-exp_binary64_1822`
3×	`associate-l_binary64_1724`
2×	`cbrt-unprod_binary64_1816` `cbrt-undiv_binary64_1817` `pow-pow_binary64_1855`
1×	`associate-/l_binary64_1728` `div-inv_binary64_1780` `-commutative_binary64_1714` `frac-2neg_binary64_1794` `clear-num_binary64_1782`

Counts

4 → 104

Calls

8 calls:

8.0ms	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
6.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
3.0ms	(pow.f64 (sin.f64 eps) 2)
2.0ms	(pow.f64 (cos.f64 eps) 2)
0.0ms	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)))

series376.0ms (0.3%)

Counts

4 → 23

Calls

4 calls:

225.0ms	(/.f64 (*.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2))
99.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
28.0ms	(pow.f64 (cos.f64 eps) 2)
24.0ms	(pow.f64 (sin.f64 eps) 2)

Compiler

Compiled 730 to 533 computations (27% saved)

simplify67.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5047	1585

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
0.3b	(cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))
0.3b	(*.f64 (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
0.2b	(.f64 (.f64 (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))
0.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.6b	(tan.f64 (+.f64 x eps))
3.6b	(tan.f64 (+.f64 x eps))
3.6b	(tan.f64 (+.f64 x eps))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 45

Calls

8 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x)))) (cbrt.f64 (-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))))

series793.0ms (0.6%)

Counts

4 → 45

Calls

4 calls:

277.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
182.0ms	(tan.f64 (+.f64 x eps))
171.0ms	(tan.f64 (+.f64 x eps))
163.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 2854 to 1533 computations (46.3% saved)

simplify47.0ms (0%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5576	2401

prune7.0s (5.2%)

Pruning

274 alts after pruning (268 fresh and 6 done)

	Pruned	Kept	Total
New	244	241	485
Fresh	7	27	34
Picked	0	0	0
Done	0	6	6
Total	251	274	525

Error

0.1b

Counts

525 → 274

Compiler

Compiled 16730 to 7424 computations (55.6% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.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))
3.3b	(-.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite52.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
27×	`times-frac_binary64_1789`
24×	`add-cube-cbrt_binary64_1818`
17×	`unpow-prod-down_binary64_1862`
11×	`add-exp-log_binary64_1821`
8×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728` `add-log-exp_binary64_1822`
7×	`tan-quot_binary64_1942`
6×	`pow1_binary64_1844`
5×	`sqr-pow_binary64_1755` `distribute-lft-out_binary64_1734`
4×	`difference-of-squares_binary64_1752`
3×	`cancel-sign-sub-inv_binary64_1749` `associate-/r_binary64_1727` `associate-l_binary64_1724` `div-exp_binary64_1834` `associate-r*_binary64_1723`
2×	`flip3--_binary64_1787` `associate-/r/_binary64_1729` `flip--_binary64_1758`
1×	`associate-r/_binary64_1725` `+-commutative_binary64_1713` `frac-add_binary64_1791` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `div-inv_binary64_1780` `distribute-lft-out--_binary64_1735` `associate-l/_binary64_1726` `diff-log_binary64_1875` `frac-sub_binary64_1792` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `frac-times_binary64_1793` `flip3-+_binary64_1786` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `pow-to-exp_binary64_1852` `sub-neg_binary64_1776` `pow-exp_binary64_1851`

Counts

4 → 105

Calls

8 calls:

20.0ms	(-.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
10.0ms	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (1.4%)

Counts

4 → 44

Calls

4 calls:

979.0ms	(-.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
546.0ms	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
227.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
203.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2096 to 1363 computations (35% saved)

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4955	4626
1	4955	4626

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.5b	(-.f64 (.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (.f64 (tan.f64 x) (tan.f64 x)))
0.4b	(*.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.1b	(+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))
2.7b	(/.f64 (-.f64 (.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
3.6b	(tan.f64 (+.f64 x eps))
3.6b	(tan.f64 (+.f64 x eps))
3.6b	(tan.f64 (+.f64 x eps))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`tan-quot_binary64_1942`
26×	`associate-/l/_binary64_1730`
24×	`*-un-lft-identity_binary64_1783` `frac-sub_binary64_1792`
22×	`tan-sum_binary64_1918`
20×	`frac-times_binary64_1793`
16×	`times-frac_binary64_1789`
14×	`associate-r/_binary64_1725` `add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `associate-l/_binary64_1726`
6×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
5×	`difference-of-squares_binary64_1752` `distribute-lft-out_binary64_1734`
4×	`associate-/r/_binary64_1729` `associate-/l_binary64_1728` `associate-/r_binary64_1727` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`frac-add_binary64_1791`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `flip-+_binary64_1757` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

4 → 94

Calls

8 calls:

24.0ms	(/.f64 (-.f64 (.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))

series1.4s (1%)

Counts

4 → 43

Calls

4 calls:

904.0ms	(/.f64 (-.f64 (.f64 (tan.f64 (+.f64 x eps)) (tan.f64 (+.f64 x eps))) (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
171.0ms	(tan.f64 (+.f64 x eps))
163.0ms	(tan.f64 (+.f64 x eps))
120.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 2508 to 1403 computations (44.1% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4969	4444
1	4969	4444

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (cos.f64 eps) (sin.f64 eps))
0.1b	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps)))
0.0b	(-.f64 (exp.f64 (+.f64 (log.f64 (/.f64 (sin.f64 eps) (cos.f64 eps))) (*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps)))))) (tan.f64 x))
0.0b	(+.f64 (log.f64 (/.f64 (sin.f64 eps) (cos.f64 eps))) (*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps)))))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps))))
0.4b	(exp.f64 (+.f64 (log.f64 (/.f64 (sin.f64 eps) (cos.f64 eps))) (*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps))))))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_1783`
25×	`add-sqr-sqrt_binary64_1805`
23×	`add-cube-cbrt_binary64_1818`
20×	`times-frac_binary64_1789`
10×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
6×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `add-log-exp_binary64_1822` `pow1_binary64_1844`
5×	`associate-r_binary64_1723`
3×	`associate-r/_binary64_1725` `associate-l*_binary64_1724` `exp-prod_binary64_1835`
2×	`quot-tan_binary64_1943` `rem-exp-log_binary64_1823` `distribute-lft-out_binary64_1734` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782`
1×	`exp-diff_binary64_1831` `exp-sum_binary64_1829` `distribute-lft-in_binary64_1732` `frac-add_binary64_1791` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `associate-+l-_binary64_1718` `*-commutative_binary64_1714` `distribute-rgt-in_binary64_1733` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `log-div_binary64_1870`

Counts

4 → 95

Calls

8 calls:

18.0ms	(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps))))
6.0ms	(exp.f64 (+.f64 (log.f64 (/.f64 (sin.f64 eps) (cos.f64 eps))) (*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps))))))
4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.0ms	(+.f64 (log.f64 (/.f64 (sin.f64 eps) (cos.f64 eps))) (*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps)))))

series604.0ms (0.4%)

Counts

4 → 22

Calls

4 calls:

288.0ms	(exp.f64 (+.f64 (log.f64 (/.f64 (sin.f64 eps) (cos.f64 eps))) (*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps))))))
250.0ms	(*.f64 x (+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (cos.f64 eps) (sin.f64 eps))))
33.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
33.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))

Compiler

Compiled 1222 to 671 computations (45.1% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5041	2258

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))
0.1b	(+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))
0.1b	(/.f64 (*.f64 x x) (cos.f64 eps))
0.0b	(+.f64 (/.f64 (.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)) (.f64 (/.f64 (*.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))))
0.3b	(pow.f64 (cos.f64 eps) 2)
0.3b	(pow.f64 (sin.f64 eps) 3)
3.1b	(*.f64 x (pow.f64 (sin.f64 eps) 2))
5.7b	(.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))))

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1805`
20×	`add-exp-log_binary64_1821`
17×	`*-un-lft-identity_binary64_1783`
16×	`add-cbrt-cube_binary64_1819`
15×	`add-cube-cbrt_binary64_1818`
12×	`associate-r_binary64_1723`
10×	`unpow-prod-down_binary64_1862` `associate-l_binary64_1724`
8×	`pow1_binary64_1844`
7×	`prod-exp_binary64_1832`
6×	`pow-unpow_binary64_1860` `unswap-sqr_binary64_1751`
5×	`cbrt-unprod_binary64_1816`
4×	`sqr-pow_binary64_1755` `times-frac_binary64_1789` `add-log-exp_binary64_1822`
3×	`unpow2_binary64_1848` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `cube-prod_binary64_1811`
2×	`associate-r/_binary64_1725` `flip-+_binary64_1757` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `div-exp_binary64_1834` `frac-times_binary64_1793` `flip3-+_binary64_1786` `pow-pow_binary64_1855`
1×	`rem-cube-cbrt_binary64_1806` `distribute-lft-in_binary64_1732` `cube-mult_binary64_1813` `distribute-lft-out_binary64_1734` `unpow3_binary64_1849` `div-inv_binary64_1780` `associate-*l/_binary64_1726` `distribute-rgt-in_binary64_1733` `pow-prod-down_binary64_1854`

Counts

4 → 103

Calls

8 calls:

37.0ms	(.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))))
7.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
3.0ms	(pow.f64 (sin.f64 eps) 3)
2.0ms	(pow.f64 (cos.f64 eps) 2)
0.0ms	(+.f64 (/.f64 (.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)) (.f64 (/.f64 (*.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))))

series562.0ms (0.4%)

Counts

4 → 20

Calls

4 calls:

391.0ms	(.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))))
105.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
43.0ms	(pow.f64 (sin.f64 eps) 3)
22.0ms	(pow.f64 (cos.f64 eps) 2)

Compiler

Compiled 1422 to 876 computations (38.4% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4968	2064
1	4968	2064

prune17.0s (12.6%)

Pruning

480 alts after pruning (469 fresh and 11 done)

	Pruned	Kept	Total
New	305	221	526
Fresh	15	248	263
Picked	0	0	0
Done	0	11	11
Total	320	480	800

Error

0.1b

Counts

800 → 480

Compiler

Compiled 28108 to 12589 computations (55.2% saved)

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.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))
3.3b	(+.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))

rewrite64.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_1783`
25×	`add-sqr-sqrt_binary64_1805`
24×	`times-frac_binary64_1789`
23×	`add-cube-cbrt_binary64_1818`
16×	`unpow-prod-down_binary64_1862`
11×	`add-exp-log_binary64_1821`
10×	`add-log-exp_binary64_1822`
8×	`add-cbrt-cube_binary64_1819` `associate-/l*_binary64_1728`
7×	`tan-quot_binary64_1942` `distribute-lft-out_binary64_1734`
6×	`pow1_binary64_1844`
4×	`sqr-pow_binary64_1755`
3×	`associate-/r_binary64_1727` `associate-l_binary64_1724` `sum-log_binary64_1874` `div-exp_binary64_1834` `associate-r*_binary64_1723`
2×	`associate-/r/_binary64_1729` `+-commutative_binary64_1713` `frac-add_binary64_1791` `flip-+_binary64_1757` `flip3-+_binary64_1786`
1×	`flip3--_binary64_1787` `associate-r/_binary64_1725` `unsub-neg_binary64_1777` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `div-inv_binary64_1780` `associate-l/_binary64_1726` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `frac-times_binary64_1793` `neg-sub0_binary64_1778` `distribute-neg-frac_binary64_1747` `neg-log_binary64_1876` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `flip--_binary64_1758` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `distribute-rgt-neg-in_binary64_1741` `associate-+r-_binary64_1717`

Counts

4 → 102

Calls

8 calls:

28.0ms	(+.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
12.0ms	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.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))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series2.0s (1.5%)

Counts

4 → 44

Calls

4 calls:

1000.0ms	(+.f64 (/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (neg.f64 (tan.f64 x)))
544.0ms	(/.f64 (pow.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) 1) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
223.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
199.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2143 to 1410 computations (34.2% saved)

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5232	4429

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/3 (pow.f64 eps 3))
0.0b	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.0b	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.1b	(*.f64 1/3 (pow.f64 eps 3))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1805`
12×	`associate-r_binary64_1723`
7×	`add-exp-log_binary64_1821`
6×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
4×	`add-cbrt-cube_binary64_1819` `unpow-prod-down_binary64_1862` `unswap-sqr_binary64_1751` `add-log-exp_binary64_1822` `cube-prod_binary64_1811`
3×	`prod-exp_binary64_1832` `associate-l_binary64_1724`
2×	`sqr-pow_binary64_1755` `pow1_binary64_1844`
1×	`+-commutative_binary64_1713` `cube-mult_binary64_1813` `cbrt-unprod_binary64_1816` `flip-+_binary64_1757` `unpow3_binary64_1849` `*-commutative_binary64_1714` `sum-log_binary64_1874` `flip3-+_binary64_1786` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`

Counts

2 → 42

Calls

4 calls:

7.0ms	(*.f64 1/3 (pow.f64 eps 3))
3.0ms	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.0ms	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
0.0ms	(*.f64 1/3 (pow.f64 eps 3))

series93.0ms (0.1%)

Counts

2 → 9

Calls

2 calls:

62.0ms	(+.f64 eps (*.f64 1/3 (pow.f64 eps 3)))
31.0ms	(*.f64 1/3 (pow.f64 eps 3))

Compiler

Compiled 95 to 98 computations (-3.2% saved)

simplify53.0ms (0%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5017	527

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps))) (pow.f64 (cos.f64 eps) (/.f64 2 2)))
0.1b	(/.f64 x (cos.f64 eps))
0.0b	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps))) (pow.f64 (cos.f64 eps) (/.f64 2 2))))
0.2b	(/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps))) (pow.f64 (cos.f64 eps) (/.f64 2 2)))
0.2b	(/.f64 (sin.f64 eps) (cos.f64 eps))
0.2b	(pow.f64 (sin.f64 eps) 2)
3.4b	(*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps)))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-exp-log_binary64_1821`
43×	`add-sqr-sqrt_binary64_1805`
34×	`div-exp_binary64_1834`
29×	`times-frac_binary64_1789`
27×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
24×	`prod-exp_binary64_1832`
20×	`add-cbrt-cube_binary64_1819`
16×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
14×	`unpow-prod-down_binary64_1862`
13×	`associate-r_binary64_1723`
10×	`associate-/r*_binary64_1727`
8×	`associate-l_binary64_1724` `unswap-sqr_binary64_1751`
6×	`sqr-pow_binary64_1755` `cbrt-undiv_binary64_1817`
5×	`pow1_binary64_1844`
4×	`associate-/l*_binary64_1728` `cbrt-unprod_binary64_1816` `unpow2_binary64_1848` `add-log-exp_binary64_1822`
3×	`pow-unpow_binary64_1860` `div-inv_binary64_1780`
2×	`associate-*r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782`
1×	`associate-/l/_binary64_1730` `quot-tan_binary64_1943` `*-commutative_binary64_1714` `pow-pow_binary64_1855`

Counts

4 → 142

Calls

8 calls:

10.0ms	(/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps))) (pow.f64 (cos.f64 eps) (/.f64 2 2)))
10.0ms	(*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps)))
4.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
3.0ms	(pow.f64 (sin.f64 eps) 2)
0.0ms	(+.f64 (/.f64 (sin.f64 eps) (cos.f64 eps)) (/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps))) (pow.f64 (cos.f64 eps) (/.f64 2 2))))

series454.0ms (0.3%)

Counts

4 → 21

Calls

4 calls:

223.0ms	(/.f64 (*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps))) (pow.f64 (cos.f64 eps) (/.f64 2 2)))
166.0ms	(*.f64 (pow.f64 (sin.f64 eps) 2) (/.f64 x (cos.f64 eps)))
41.0ms	(/.f64 (sin.f64 eps) (cos.f64 eps))
24.0ms	(pow.f64 (sin.f64 eps) 2)

Compiler

Compiled 829 to 594 computations (28.3% saved)

simplify91.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	2518
1	4965	2518

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))
0.1b	(sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
0.1b	(sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))
1.0b	(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) 2) (pow.f64 (tan.f64 x) 2)) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))))
3.6b	(tan.f64 (+.f64 x eps))
3.6b	(tan.f64 (+.f64 x eps))
3.6b	(tan.f64 (+.f64 x eps))

rewrite79.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

184×	`add-sqr-sqrt_binary64_1805`
147×	`times-frac_binary64_1789`
132×	`*-un-lft-identity_binary64_1783`
128×	`difference-of-squares_binary64_1752`
88×	`sqrt-prod_binary64_1799`
80×	`unpow-prod-down_binary64_1862`
64×	`sqr-pow_binary64_1755` `unpow2_binary64_1848`
56×	`add-cube-cbrt_binary64_1818`
22×	`distribute-lft-out_binary64_1734`
21×	`associate-/l*_binary64_1728`
16×	`distribute-lft-out--_binary64_1735`
7×	`associate-/r*_binary64_1727`
6×	`add-cbrt-cube_binary64_1819` `tan-quot_binary64_1942` `add-exp-log_binary64_1821`
4×	`associate-/r/_binary64_1729` `tan-sum_binary64_1918` `sqrt-div_binary64_1800` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`associate-/l/_binary64_1730` `frac-add_binary64_1791`
1×	`flip3--_binary64_1787` `div-sub_binary64_1788` `flip-+_binary64_1757` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782` `flip--_binary64_1758`

Counts

4 → 221

Calls

8 calls:

30.0ms	(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) 2) (pow.f64 (tan.f64 x) 2)) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))))
5.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
4.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps))))

series2.1s (1.5%)

Counts

4 → 39

Calls

4 calls:

1.6s	(/.f64 (-.f64 (pow.f64 (tan.f64 (+.f64 x eps)) 2) (pow.f64 (tan.f64 x) 2)) (sqrt.f64 (+.f64 (tan.f64 x) (tan.f64 (+.f64 x eps)))))
174.0ms	(tan.f64 (+.f64 x eps))
171.0ms	(tan.f64 (+.f64 x eps))
116.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 3902 to 2472 computations (36.6% saved)

simplify177.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4957	11538
1	4957	11538

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))
0.1b	(/.f64 (*.f64 x x) (cos.f64 eps))
0.1b	(pow.f64 (.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))) 3)
0.0b	(+.f64 (/.f64 (.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)) (cbrt.f64 (pow.f64 (.f64 (/.f64 (*.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))) 3)))
0.3b	(pow.f64 (sin.f64 eps) 3)
3.1b	(*.f64 x (pow.f64 (sin.f64 eps) 2))
5.7b	(.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))))
23.3b	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))) 3))

rewrite74.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1805`
19×	`add-exp-log_binary64_1821`
16×	`add-cbrt-cube_binary64_1819` `*-un-lft-identity_binary64_1783`
14×	`add-cube-cbrt_binary64_1818`
12×	`associate-r_binary64_1723`
10×	`associate-l_binary64_1724`
8×	`cbrt-prod_binary64_1814` `unpow-prod-down_binary64_1862`
7×	`prod-exp_binary64_1832` `pow1_binary64_1844`
6×	`unswap-sqr_binary64_1751`
5×	`cbrt-unprod_binary64_1816` `cbrt-div_binary64_1815` `cube-div_binary64_1812`
4×	`associate-*r/_binary64_1725` `sqr-pow_binary64_1755` `flip-+_binary64_1757` `times-frac_binary64_1789` `frac-times_binary64_1793` `flip3-+_binary64_1786` `add-log-exp_binary64_1822` `cube-prod_binary64_1811`
3×	`pow-unpow_binary64_1860`
2×	`cube-mult_binary64_1813` `unpow2_binary64_1848` `unpow3_binary64_1849` `associate-l/_binary64_1726` `cbrt-undiv_binary64_1817` `-commutative_binary64_1714` `div-exp_binary64_1834` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851`
1×	`rem-cbrt-cube_binary64_1807` `rem-cube-cbrt_binary64_1806` `distribute-lft-in_binary64_1732` `distribute-lft-out_binary64_1734` `div-inv_binary64_1780` `distribute-rgt-in_binary64_1733` `pow-pow_binary64_1855` `pow1/3_binary64_1865` `pow-prod-down_binary64_1854`

Counts

4 → 107

Calls

8 calls:

43.0ms	(.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))))
6.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
6.0ms	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))) 3))
3.0ms	(pow.f64 (sin.f64 eps) 3)
0.0ms	(+.f64 (/.f64 (.f64 x (pow.f64 (sin.f64 eps) 2)) (pow.f64 (cos.f64 eps) 2)) (cbrt.f64 (pow.f64 (.f64 (/.f64 (*.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))) 3)))

series923.0ms (0.7%)

Counts

4 → 23

Calls

4 calls:

392.0ms	(cbrt.f64 (pow.f64 (.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2)))) 3))
383.0ms	(.f64 (/.f64 (.f64 x x) (cos.f64 eps)) (+.f64 (sin.f64 eps) (/.f64 (pow.f64 (sin.f64 eps) 3) (pow.f64 (cos.f64 eps) 2))))
107.0ms	(*.f64 x (pow.f64 (sin.f64 eps) 2))
41.0ms	(pow.f64 (sin.f64 eps) 3)

Compiler

Compiled 1724 to 1109 computations (35.7% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4968	3151
1	4968	3151

prune28.2s (20.9%)

Pruning

738 alts after pruning (723 fresh and 15 done)

	Pruned	Kept	Total
New	458	292	750
Fresh	33	431	464
Picked	0	0	0
Done	1	15	16
Total	492	738	1230

Error

0.1b

Counts

1230 → 738

Compiler

Compiled 15030 to 5789 computations (61.5% saved)

simplify800.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5031	55676

regimes12.9s (9.5%)

Compiler: Compiled 77970 to 43677 computations (44% saved)

bsearch138.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	4.903921111721757e-06
11	-6982862.103517718	-6.07388974012318e-19	-4.406472418576731e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes12.5s (9.2%)

Compiler: Compiled 62820 to 35253 computations (43.9% saved)

bsearch120.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	2.1106641687023677e-07
11	-6982862.103517718	-6.07388974012318e-19	-2.877889322174695e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes4.3s (3.2%)

Compiler: Compiled 19490 to 12447 computations (36.1% saved)

bsearch96.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	2.1106641687023677e-07
11	-6982862.103517718	-6.07388974012318e-19	-1.3224501117002462e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.8s (2.8%)

Compiler: Compiled 15659 to 10314 computations (34.1% saved)

bsearch89.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	4.948638247358394e-09
11	-6982862.103517718	-6.07388974012318e-19	-4.735739348028543e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.2s (2.3%)

Compiler: Compiled 15389 to 10176 computations (33.9% saved)

bsearch88.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	4.347937839294806e-09
11	-6982862.103517718	-6.07388974012318e-19	-5.947394389597907e-09

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes491.0ms (0.4%)

Compiler: Compiled 2293 to 1957 computations (14.7% saved)

bsearch79.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	4.750141807257479e-06
11	-6982862.103517718	-6.07388974012318e-19	-3.7861050372932166e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes474.0ms (0.4%)

Compiler: Compiled 2197 to 1885 computations (14.2% saved)

bsearch73.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	3.6673023185841255e-06
11	-6982862.103517718	-6.07388974012318e-19	-2.1161599242012276e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes335.0ms (0.2%)

Compiler: Compiled 1291 to 1186 computations (8.1% saved)

bsearch68.0ms (0.1%)

Steps

Iters	Range		Point
8	3.6987200893425924e-09	4.980810763953897e-06	1.903094475028712e-06
11	-6982862.103517718	-6.07388974012318e-19	-3.1686865321513423e-07

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes205.0ms (0.2%)

Compiler: Compiled 1213 to 1114 computations (8.2% saved)

bsearch0.0ms (0%)

regimes35.0ms (0%)

Compiler: Compiled 48 to 58 computations (-20.8% saved)

bsearch67.0ms (0%)

Steps

Iters	Range		Point
8	3.059832913184538e+35	2.530612389084193e+39	3.3880205997539494e+35
11	-6982862.103517718	-6.07388974012318e-19	-2.3558768098808724

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes29.0ms (0%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch62.0ms (0%)

Steps

Iters	Range		Point
8	3.059832913184538e+35	2.530612389084193e+39	5.605199843625231e+38
11	-6982862.103517718	-6.07388974012318e-19	-2.3558768098808724

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes17.0ms (0%)

Accuracy

Total 0.2b remaining (73.7%)

Threshold costs 0.2b (73.7%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch24.0ms (0%)

Compiler: Compiled 547 to 309 computations (43.5% saved)

simplify13.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	210	811
1	210	811

end0.0ms (0%)

sample24.6s (18.2%)

Algorithm

1×

intervals

Results

905.0ms	3527×	body	1024	valid
552.0ms	1189×	body	2048	valid
222.0ms	1381×	body	512	valid
64.0ms	592×	body	256	valid
63.0ms	1309×	body	128	valid
2.0ms	2×	body	4096	valid

Compiler

Compiled 26938 to 15130 computations (43.8% saved)

Pareto

0.7794521891773362