Details

analyze832.0ms (11.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample75.0ms (1.1%)

Algorithm

1×

intervals

Results

39.0ms	63×	body	1024	valid
14.0ms	142×	body	128	valid
11.0ms	32×	body	512	valid
4.0ms	19×	body	256	valid

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	50	22
1	50	22

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.4b

Counts

2 → 1

Compiler

Compiled 58 to 50 computations (13.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
0.3b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
14.2b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

9.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
5.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series213.0ms (3%)

Counts

3 → 9

Calls

3 calls:

128.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
52.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
33.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

simplify84.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4918	1066
1	4918	1066

prune509.0ms (7.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	54	14	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	14	69

Merged error: 0.1b

Counts

69 → 14

Compiler

Compiled 7399 to 6045 computations (18.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
0.3b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `times-frac_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/r*_binary64` `add-log-exp_binary64`
2×	`pow-prod-down_binary64` `unswap-sqr_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

3 → 66

Calls

3 calls:

10.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
6.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

series244.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

125.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
84.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
36.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

simplify71.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4928	1245
1	4928	1245

prune413.0ms (5.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	8	5	13
Picked	0	1	1
Done	0	0	0
Total	76	13	89

Merged error: 0.0b

Counts

89 → 13

Compiler

Compiled 6116 to 5103 computations (16.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))
0.3b	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
0.3b	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`
19×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
13×	`pow1_binary64`
7×	`associate-l_binary64` `sqrt-prod_binary64`
6×	`cbrt-undiv_binary64` `times-frac_binary64` `div-exp_binary64`
5×	`pow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r_binary64` `unswap-sqr_binary64` `-commutative_binary64`
2×	`div-inv_binary64`
1×	`associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`

Counts

4 → 95

Calls

4 calls:

13.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
10.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
10.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

series463.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x)))
151.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
84.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
51.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

simplify95.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4906	1758
1	4906	1758

prune201.0ms (2.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	109	11	120

Merged error: 0.0b

Counts

120 → 11

Compiler

Compiled 3189 to 2546 computations (20.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.8b	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64`
38×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
36×	`associate-r_binary64`
28×	`unpow-prod-down_binary64` `cube-prod_binary64`
17×	`add-exp-log_binary64`
10×	`add-cbrt-cube_binary64`
7×	`pow1_binary64` `unswap-sqr_binary64`
6×	`associate-l_binary64`
5×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `cube-div_binary64` `div-inv_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64`
2×	`cbrt-div_binary64` `pow-to-exp_binary64` `cbrt-unprod_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `cbrt-prod_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `pow-pow_binary64`

Counts

4 → 131

Calls

4 calls:

15.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
7.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))
6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
6.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)

series594.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
151.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
117.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
117.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

simplify58.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5111	2969

prune358.0ms (5.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	2	6	8
Picked	0	1	1
Done	0	2	2
Total	143	11	154

Merged error: 0b

Counts

154 → 11

Compiler

Compiled 5644 to 4492 computations (20.4% saved)

regimes30.0ms (0.4%)

Compiler: Compiled 230 to 200 computations (13% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	13	22

end0.0ms (0%)

sample2.6s (36.9%)

Algorithm

1×

intervals

Results

1.2s	2039×	body	1024	valid
498.0ms	4480×	body	128	valid
332.0ms	968×	body	512	valid
115.0ms	505×	body	256	valid
10.0ms	8×	body	2048	valid

Compiler

Compiled 275 to 240 computations (12.7% saved)

Details

analyze832.0ms (11.8%)

sample75.0ms (1.1%)

simplify8.0ms (0.1%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite27.0ms (0.4%)

series213.0ms (3%)

simplify84.0ms (1.2%)

prune509.0ms (7.2%)

localize10.0ms (0.1%)

rewrite26.0ms (0.4%)

series244.0ms (3.5%)

simplify71.0ms (1%)

prune413.0ms (5.9%)

localize12.0ms (0.2%)

rewrite49.0ms (0.7%)

series463.0ms (6.6%)

simplify95.0ms (1.3%)

prune201.0ms (2.8%)

localize12.0ms (0.2%)

rewrite48.0ms (0.7%)

series594.0ms (8.4%)

simplify58.0ms (0.8%)

prune358.0ms (5.1%)

regimes30.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (36.9%)

Profiling