Details

analyze1.2s (3.8%)

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 13 to 12 computations (7.7% saved)

sample95.0ms (0.3%)

Algorithm

1×

intervals

Results

38.0ms	68×	body	1024	valid
16.0ms	121×	body	128	valid
15.0ms	42×	body	512	valid
6.0ms	25×	body	256	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 25 to 25 computations (0% saved)

simplify155.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	140	14
1	140	14

prune8.0ms (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: 0.1b

Counts

2 → 2

Compiler

Compiled 30 to 27 computations (10% saved)

localize11.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`
9×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r_binary64` `difference-of-squares_binary64` `associate-/l_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`distribute-lft-out--_binary64` `div-exp_binary64`
2×	`cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `inv-pow_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`

Counts

3 → 94

Calls

3 calls:

25.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
10.0ms	(/.f64 x (tan.f64 B))
7.0ms	(/.f64 1 (sin.f64 B))

series346.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

176.0ms	(/.f64 x (tan.f64 B))
146.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
23.0ms	(/.f64 1 (sin.f64 B))

simplify92.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4891	1413
1	4891	1413

prune426.0ms (1.4%)

Pruning

38 alts after pruning (37 fresh and 1 done)

	Pruned	Kept	Total
New	67	36	103
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	38	105

Merged error: 0.0b

Counts

105 → 38

Compiler

Compiled 2102 to 1022 computations (51.4% saved)

localize26.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1))) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1)))
0.2b	(/.f64 x (tan.f64 B))

rewrite134.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`times-frac_binary64`
73×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
44×	`add-cube-cbrt_binary64`
25×	`associate-/r*_binary64`
22×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
14×	`cancel-sign-sub-inv_binary64`
11×	`add-cbrt-cube_binary64`
10×	`difference-of-squares_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64` `div-inv_binary64`
4×	`associate-/l*_binary64`
3×	`pow1_binary64` `associate-/r/_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

3 → 129

Calls

3 calls:

73.0ms	(-.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1))) (/.f64 x (tan.f64 B)))
23.0ms	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1)))
9.0ms	(/.f64 x (tan.f64 B))

series401.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

204.0ms	(-.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1))) (/.f64 x (tan.f64 B)))
156.0ms	(/.f64 x (tan.f64 B))
41.0ms	(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1)))

simplify133.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5102	2641

prune967.0ms (3.2%)

Pruning

81 alts after pruning (79 fresh and 2 done)

	Pruned	Kept	Total
New	91	47	138
Fresh	4	32	36
Picked	0	1	1
Done	0	1	1
Total	95	81	176

Merged error: 0.0b

Counts

176 → 81

Compiler

Compiled 4592 to 2929 computations (36.2% saved)

localize12.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 1) (/.f64 (sin.f64 B) (cbrt.f64 1)))) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 (cbrt.f64 1) (/.f64 (sin.f64 B) (cbrt.f64 1)))
0.2b	(/.f64 x (tan.f64 B))

rewrite75.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

276×	`times-frac_binary64`
155×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
132×	`cbrt-prod_binary64`
25×	`associate-/r*_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`add-exp-log_binary64` `div-inv_binary64`
9×	`associate-/l*_binary64`
7×	`add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `associate-/r/_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `tan-quot_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-*r/_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

3 → 229

Calls

3 calls:

30.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 1) (/.f64 (sin.f64 B) (cbrt.f64 1)))) (/.f64 x (tan.f64 B)))
11.0ms	(/.f64 (cbrt.f64 1) (/.f64 (sin.f64 B) (cbrt.f64 1)))
4.0ms	(/.f64 x (tan.f64 B))

series304.0ms (1%)

Counts

3 → 9

Calls

3 calls:

143.0ms	(/.f64 x (tan.f64 B))
132.0ms	(-.f64 (.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (cbrt.f64 1) (/.f64 (sin.f64 B) (cbrt.f64 1)))) (/.f64 x (tan.f64 B)))
28.0ms	(/.f64 (cbrt.f64 1) (/.f64 (sin.f64 B) (cbrt.f64 1)))

simplify229.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	4903	5733
1	4903	5733

prune3.3s (10.9%)

Pruning

126 alts after pruning (123 fresh and 3 done)

	Pruned	Kept	Total
New	181	57	238
Fresh	12	66	78
Picked	0	1	1
Done	0	2	2
Total	193	126	319

Merged error: 0.0b

Counts

319 → 126

Compiler

Compiled 9704 to 6943 computations (28.5% saved)

localize27.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1))) (/.f64 (neg.f64 x) (tan.f64 B)))

0.1b

(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1)))

0.2b

(/.f64 (neg.f64 x) (tan.f64 B))

rewrite119.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

88×	`times-frac_binary64`
54×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
25×	`associate-/r*_binary64`
18×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
12×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`add-log-exp_binary64`
4×	`neg-mul-1_binary64` `div-inv_binary64`
3×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `neg-sub0_binary64` `associate-/r/_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-frac-neg_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `frac-add_binary64` `+-commutative_binary64` `flip-+_binary64` `unsub-neg_binary64` `tan-quot_binary64` `sum-log_binary64`

Counts

3 → 137

Calls

3 calls:

74.0ms

(+.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1))) (/.f64 (neg.f64 x) (tan.f64 B)))

15.0ms

(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1)))

9.0ms

(/.f64 (neg.f64 x) (tan.f64 B))

series337.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

164.0ms

(+.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1))) (/.f64 (neg.f64 x) (tan.f64 B)))

137.0ms

(/.f64 (neg.f64 x) (tan.f64 B))

35.0ms

(/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) (/.f64 (sin.f64 B) (cbrt.f64 1)))

simplify126.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4973	2604
1	4973	2604

prune1.9s (6.1%)

Pruning

141 alts after pruning (137 fresh and 4 done)

	Pruned	Kept	Total
New	113	33	146
Fresh	18	104	122
Picked	0	1	1
Done	0	3	3
Total	131	141	272

Merged error: 0.0b

Counts

272 → 141

Compiler

Compiled 3151 to 1702 computations (46% saved)

regimes4.0s (13.1%)

Compiler: Compiled 26830 to 22341 computations (16.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	26
1	30	26

end0.0ms (0%)

sample16.0s (52.7%)

Algorithm

1×

intervals

Results

909.0ms	2253×	body	1024	valid
454.0ms	3980×	body	128	valid
347.0ms	1187×	body	512	valid
116.0ms	576×	body	256	valid
18.0ms	170×	body	128	invalid
2.0ms	4×	body	2048	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 8963 to 7466 computations (16.7% saved)

Pareto

Details

analyze1.2s (3.8%)

sample95.0ms (0.3%)

simplify155.0ms (0.5%)

prune8.0ms (0%)

localize11.0ms (0%)

rewrite50.0ms (0.2%)

series346.0ms (1.1%)

simplify92.0ms (0.3%)

prune426.0ms (1.4%)

localize26.0ms (0.1%)

rewrite134.0ms (0.4%)

series401.0ms (1.3%)

simplify133.0ms (0.4%)

prune967.0ms (3.2%)

localize12.0ms (0%)

rewrite75.0ms (0.2%)

series304.0ms (1%)

simplify229.0ms (0.8%)

prune3.3s (10.9%)

localize27.0ms (0.1%)

rewrite119.0ms (0.4%)

series337.0ms (1.1%)

simplify126.0ms (0.4%)

prune1.9s (6.1%)

regimes4.0s (13.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample16.0s (52.7%)

Profiling