Details

analyze231.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample51.0ms (1.2%)

Algorithm

1×

intervals

Results

24.0ms	56×	body	2048	valid
8.0ms	45×	body	1024	valid
6.0ms	48×	body	512	valid
3.0ms	77×	body	128	valid
2.0ms	28×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify23.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	364	12
1	364	12

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: 31.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.4b	(-.f64 1 (cos.f64 x))
13.1b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64`
5×	`add-cube-cbrt_binary64`
4×	`add-log-exp_binary64`
3×	`cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

2 → 47

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series82.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms	(-.f64 1 (cos.f64 x))

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4889	715
1	4889	715

prune223.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	46	7	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 0.0b

Counts

54 → 7

Compiler

Compiled 3383 to 2224 computations (34.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.6b	(+.f64 1 (cos.f64 x))
13.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite41.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`cbrt-undiv_binary64` `div-exp_binary64`
11×	`pow1_binary64` `associate-/l*_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `div-sub_binary64` `sqr-sin-a_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 111

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series249.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
86.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
29.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4975	1783
1	4975	1783

prune158.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	124	6	130

Merged error: 0b

Counts

130 → 6

Compiler

Compiled 2978 to 1655 computations (44.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64` `associate-l_binary64`
6×	`associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-exp_binary64`
5×	`pow1_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64`
3×	`add-log-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `frac-times_binary64` `tan-quot_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 105

Calls

3 calls:

12.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

series282.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

143.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
105.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
34.0ms	(/.f64 (sin.f64 x) x)

simplify93.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5003	1953

prune100.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	114	6	120

Merged error: 0b

Counts

120 → 6

Compiler

Compiled 2061 to 1060 computations (48.6% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
13.1b	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
13.1b	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`pow1_binary64`
32×	`sqrt-pow1_binary64`
30×	`sqrt-div_binary64`
22×	`pow-prod-down_binary64`
19×	`frac-times_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`associate-r/_binary64` `associate-l/_binary64`
12×	`pow1/2_binary64`
10×	`pow-prod-up_binary64`
9×	`times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow-sqr_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
1×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow2_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 120

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
6.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
6.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

series624.0ms (14%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
176.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
145.0ms	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
104.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

simplify58.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5095	2351

prune190.0ms (4.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	132	6	138

Merged error: 0b

Counts

138 → 6

Compiler

Compiled 3200 to 1862 computations (41.8% saved)

regimes14.0ms (0.3%)

Compiler: Compiled 85 to 62 computations (27.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample1.8s (39.7%)

Algorithm

1×

intervals

Results

863.0ms	2036×	body	2048	valid
225.0ms	1122×	body	1024	valid
197.0ms	1462×	body	512	valid
102.0ms	2537×	body	128	valid
67.0ms	734×	body	256	valid
44.0ms	109×	body	4096	valid

Compiler

Compiled 103 to 76 computations (26.2% saved)

Details

analyze231.0ms (5.2%)

sample51.0ms (1.2%)

simplify23.0ms (0.5%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite17.0ms (0.4%)

series82.0ms (1.8%)

simplify58.0ms (1.3%)

prune223.0ms (5%)

localize13.0ms (0.3%)

rewrite41.0ms (0.9%)

series249.0ms (5.6%)

simplify64.0ms (1.4%)

prune158.0ms (3.5%)

localize9.0ms (0.2%)

rewrite30.0ms (0.7%)

series282.0ms (6.3%)

simplify93.0ms (2.1%)

prune100.0ms (2.3%)

localize12.0ms (0.3%)

rewrite48.0ms (1.1%)

series624.0ms (14%)

simplify58.0ms (1.3%)

prune190.0ms (4.3%)

regimes14.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.8s (39.7%)

Profiling