Details

analyze741.0ms (8.1%)

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)

sample89.0ms (1%)

Algorithm

1×

intervals

Results

40.0ms	123×	body	1024	valid
31.0ms	36×	body	2048	valid
7.0ms	42×	body	512	valid
2.0ms	44×	body	128	valid
1.0ms	11×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

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

Merged error: 37.8b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.6b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.7b	(tan.f64 (+.f64 x eps))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `tan-quot_binary64`
2×	`tan-sum_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

2 → 24

Calls

2 calls:

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

series340.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

213.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
127.0ms	(tan.f64 (+.f64 x eps))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4932	529
1	4932	529

prune36.0ms (0.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.5b

Counts

31 → 7

Compiler

Compiled 529 to 172 computations (67.5% saved)

localize11.0ms (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))
1.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`tan-quot_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

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))))
7.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

series1.9s (20.6%)

Counts

4 → 12

Calls

4 calls:

948.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
549.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
197.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
185.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5065	2549

prune126.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	88	9	97
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 14.4b

Counts

104 → 11

Compiler

Compiled 2760 to 920 computations (66.7% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
1.4b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
5×	`cbrt-unprod_binary64` `prod-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `tan-quot_binary64`
2×	`difference-of-squares_binary64` `sin-mult_binary64` `times-frac_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cos-mult_binary64` `frac-add_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

25.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
8.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

series1.4s (15.6%)

Counts

4 → 12

Calls

4 calls:

964.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
209.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
186.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
68.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4983	1982
1	4983	1982

prune103.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 12.4b

Counts

93 → 9

Compiler

Compiled 2650 to 741 computations (72% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 x) (cos.f64 x))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
2.0b	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `difference-of-sqr--1_binary64`
2×	`associate-/l/_binary64` `distribute-lft-out_binary64` `cos-mult_binary64` `associate-/r/_binary64` `sin-mult_binary64`
1×	`flip3-+_binary64` `quot-tan_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 90

Calls

4 calls:

17.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
8.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
4.0ms	(/.f64 (sin.f64 x) (cos.f64 x))

series779.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

350.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)
189.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
187.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
53.0ms	(/.f64 (sin.f64 x) (cos.f64 x))

simplify72.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4958	2190
1	4958	2190

prune153.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	101	10	111

Merged error: 12.4b

Counts

111 → 10

Compiler

Compiled 4950 to 1518 computations (69.3% saved)

regimes65.0ms (0.7%)

Compiler: Compiled 814 to 432 computations (46.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	70
1	58	70

end0.0ms (0%)

sample2.8s (30.6%)

Algorithm

1×

intervals

Results

1.1s	3514×	body	1024	valid
831.0ms	1171×	body	2048	valid
237.0ms	1430×	body	512	valid
64.0ms	585×	body	256	valid
60.0ms	1297×	body	128	valid
5.0ms	3×	body	4096	valid

Compiler

Compiled 466 to 251 computations (46.1% saved)

Details

analyze741.0ms (8.1%)

sample89.0ms (1%)

simplify11.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite13.0ms (0.1%)

series340.0ms (3.7%)

simplify85.0ms (0.9%)

prune36.0ms (0.4%)

localize11.0ms (0.1%)

rewrite44.0ms (0.5%)

series1.9s (20.6%)

simplify79.0ms (0.9%)

prune126.0ms (1.4%)

localize22.0ms (0.2%)

rewrite52.0ms (0.6%)

series1.4s (15.6%)

simplify115.0ms (1.3%)

prune103.0ms (1.1%)

localize22.0ms (0.2%)

rewrite51.0ms (0.6%)

series779.0ms (8.5%)

simplify72.0ms (0.8%)

prune153.0ms (1.7%)

regimes65.0ms (0.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.8s (30.6%)

Profiling