Details

analyze1.2s (6.6%)

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)

sample110.0ms (0.6%)

Algorithm

1×

intervals

Results

48.0ms	44×	body	2048	valid
34.0ms	110×	body	1024	valid
8.0ms	44×	body	512	valid
3.0ms	20×	body	256	valid
2.0ms	38×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune2.0ms (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

38.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.5b	(tan.f64 (+.f64 x eps))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

22.7b

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)

series571.0ms (3.2%)

Error

12.7b

Counts

2 → 24

Calls

2 calls:

302.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
220.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 1700 to 1001 computations (41.1% saved)

simplify44.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5501	1566

prune82.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	3	52

Error

0.3b

Counts

52 → 3

Compiler

Compiled 1273 to 514 computations (59.6% 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))
3.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite154.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

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:

18.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
8.0ms	(/.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))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2365 to 732 computations (69% saved)

series2.4s (13.4%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

1.2s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
606.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
296.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
211.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 3708 to 2008 computations (45.8% saved)

simplify92.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5196	4229

prune231.0ms (1.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	125	11	136
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	126	13	139

Error

0.1b

Counts

139 → 13

Compiler

Compiled 4306 to 1572 computations (63.5% saved)

localize22.0ms (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))
0.3b	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
3.6b	(-.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))

rewrite165.0ms (0.9%)

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:

20.0ms	(-.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))
14.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
9.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 2368 to 588 computations (75.2% saved)

series1.8s (10.4%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

1.1s	(-.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))
337.0ms	(/.f64 (.f64 (sin.f64 eps) (sin.f64 x)) (.f64 (cos.f64 eps) (cos.f64 x)))
231.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
118.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 3676 to 1942 computations (47.2% saved)

simplify126.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4976	3312
1	4976	3312

prune186.0ms (1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	115	5	120
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	120	13	133

Error

0.1b

Counts

133 → 13

Compiler

Compiled 4339 to 1422 computations (67.2% saved)

localize20.0ms (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))
3.5b	(log.f64 (exp.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
3.6b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (log.f64 (exp.f64 (.f64 (sin.f64 eps) (sin.f64 x)))) (.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))

rewrite138.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_1805`
12×	`*-un-lft-identity_binary64_1783`
9×	`add-log-exp_binary64_1822`
8×	`add-cube-cbrt_binary64_1818`
7×	`pow1_binary64_1844`
6×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
3×	`tan-quot_binary64_1942` `cancel-sign-sub-inv_binary64_1749` `log-pow_binary64_1872` `log-prod_binary64_1869` `associate-l_binary64_1724` `associate-r_binary64_1723`
2×	`difference-of-squares_binary64_1752`
1×	`diff-log_binary64_1875` `frac-sub_binary64_1792` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `times-frac_binary64_1789` `distribute-lft-out--_binary64_1735` `exp-to-pow_binary64_1845` `exp-prod_binary64_1835` `rem-log-exp_binary64_1824` `sin-mult_binary64_1938` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `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 → 64

Calls

4 calls:

20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (log.f64 (exp.f64 (.f64 (sin.f64 eps) (sin.f64 x)))) (.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
5.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))
4.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))

Compiler

Compiled 2201 to 566 computations (74.3% saved)

series2.3s (13.2%)

Error

0.1b

Counts

4 → 46

Calls

4 calls:

1.4s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (log.f64 (exp.f64 (.f64 (sin.f64 eps) (sin.f64 x)))) (.f64 (cos.f64 eps) (cos.f64 x))))) (tan.f64 x))
418.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 eps) (sin.f64 x))))
247.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
154.0ms	(*.f64 (sin.f64 eps) (sin.f64 x))

Compiler

Compiled 3786 to 2031 computations (46.4% saved)

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5421	2820

prune154.0ms (0.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	110	13	123

Error

0.1b

Counts

123 → 13

Compiler

Compiled 3495 to 1050 computations (70% saved)

regimes1.6s (9.3%)

Accuracy

Total 0.2b remaining (62.9%)

Threshold costs 0.2b (62.9%)

Compiler

Compiled 11792 to 6887 computations (41.6% saved)

bsearch98.0ms (0.6%)

Steps

Iters	Range		Point
9	7.063657168295903e-09	0.030965969165772503	0.0002144194778667246
7	-0.0004632039719346494	-2.5005587671238633e-05	-0.00015670222871752272

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	120	235
1	120	235

end0.0ms (0%)

sample6.0s (33.9%)

Algorithm

1×

intervals

Results

1.1s	3548×	body	1024	valid
710.0ms	1212×	body	2048	valid
253.0ms	1369×	body	512	valid
75.0ms	563×	body	256	valid
71.0ms	1305×	body	128	valid
3.0ms	3×	body	4096	valid

Compiler

Compiled 4068 to 2383 computations (41.4% saved)

Details

analyze1.2s (6.6%)

sample110.0ms (0.6%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0%)

rewrite65.0ms (0.4%)

series571.0ms (3.2%)

simplify44.0ms (0.2%)

prune82.0ms (0.5%)

localize10.0ms (0.1%)

rewrite154.0ms (0.9%)

series2.4s (13.4%)

simplify92.0ms (0.5%)

prune231.0ms (1.3%)

localize22.0ms (0.1%)

rewrite165.0ms (0.9%)

series1.8s (10.4%)

simplify126.0ms (0.7%)

prune186.0ms (1%)

localize20.0ms (0.1%)

rewrite138.0ms (0.8%)

series2.3s (13.2%)

simplify69.0ms (0.4%)

prune154.0ms (0.9%)

regimes1.6s (9.3%)

bsearch98.0ms (0.6%)

simplify5.0ms (0%)

end0.0ms (0%)

sample6.0s (33.9%)

Profiling