Details

analyze850.0ms (11.7%)

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%)

Algorithm

1×

intervals

Results

39.0ms	70×	body	1024	valid
14.0ms	137×	body	128	valid
10.0ms	30×	body	512	valid
4.0ms	19×	body	256	valid

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify187.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 17.3b

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))))
0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
17.1b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_16285` `add-cbrt-cube_binary64_16283`
10×	`pow1_binary64_16308` `add-sqr-sqrt_binary64_16269`
8×	`*-un-lft-identity_binary64_16247` `add-cube-cbrt_binary64_16282`
7×	`cbrt-unprod_binary64_16280` `prod-exp_binary64_16296`
6×	`associate-l_binary64_16188`
4×	`pow-prod-down_binary64_16318` `associate-r_binary64_16187`
3×	`add-log-exp_binary64_16286` `times-frac_binary64_16253` `div-exp_binary64_16298` `associate-/r*_binary64_16191` `cbrt-undiv_binary64_16281`
2×	`*-commutative_binary64_16178`
1×	`clear-num_binary64_16246` `associate-/l*_binary64_16192` `frac-2neg_binary64_16258` `unswap-sqr_binary64_16215` `div-inv_binary64_16244`

Counts

3 → 59

Calls

3 calls:

10.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
8.0ms	(.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)))

series204.0ms (2.8%)

Counts

3 → 9

Calls

3 calls:

121.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
53.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
30.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

simplify85.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4918	1066
1	4918	1066

prune465.0ms (6.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	55	13	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	13	69

Merged error: 0.1b

Counts

69 → 13

Compiler

Compiled 6621 to 5400 computations (18.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
0.4b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_16285` `add-cbrt-cube_binary64_16283`
14×	`add-sqr-sqrt_binary64_16269`
10×	`-un-lft-identity_binary64_16247` `add-cube-cbrt_binary64_16282` `associate-r*_binary64_16187`
7×	`pow1_binary64_16308`
6×	`cbrt-unprod_binary64_16280` `times-frac_binary64_16253` `prod-exp_binary64_16296` `associate-l_binary64_16188`
4×	`div-exp_binary64_16298` `cbrt-undiv_binary64_16281`
3×	`add-log-exp_binary64_16286` `associate-/r*_binary64_16191`
2×	`pow-prod-down_binary64_16318` `unswap-sqr_binary64_16215` `*-commutative_binary64_16178` `div-inv_binary64_16244`
1×	`clear-num_binary64_16246` `associate-/l_binary64_16192` `frac-2neg_binary64_16258` `associate-r/_binary64_16189`

Counts

3 → 66

Calls

3 calls:

13.0ms	(.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)

series222.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

113.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
78.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
30.0ms	(.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	4929	1245
1	4929	1245

prune417.0ms (5.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	68	7	75
Fresh	7	5	12
Picked	0	1	1
Done	0	0	0
Total	75	13	88

Merged error: 0.0b

Counts

88 → 13

Compiler

Compiled 6198 to 5134 computations (17.2% 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))
0.2b	(.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))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_16285` `add-cbrt-cube_binary64_16283`
20×	`add-sqr-sqrt_binary64_16269`
19×	`associate-r_binary64_16187`
14×	`cbrt-unprod_binary64_16280` `prod-exp_binary64_16296` `*-un-lft-identity_binary64_16247` `add-cube-cbrt_binary64_16282`
13×	`pow1_binary64_16308`
7×	`sqrt-prod_binary64_16263` `associate-l_binary64_16188`
6×	`times-frac_binary64_16253` `div-exp_binary64_16298` `cbrt-undiv_binary64_16281`
5×	`pow-prod-down_binary64_16318`
4×	`add-log-exp_binary64_16286`
3×	`unswap-sqr_binary64_16215` `-commutative_binary64_16178` `associate-/r_binary64_16191`
2×	`div-inv_binary64_16244`
1×	`clear-num_binary64_16246` `associate-/l_binary64_16192` `frac-2neg_binary64_16258` `associate-r/_binary64_16189`

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)))
11.0ms	(/.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))
7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

series465.0ms (6.4%)

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)))
148.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
82.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
58.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

simplify80.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4905	1758
1	4905	1758

prune312.0ms (4.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	2	9	11
Picked	0	1	1
Done	1	0	1
Total	107	13	120

Merged error: 0.0b

Counts

120 → 13

Compiler

Compiled 4701 to 3814 computations (18.9% saved)

localize13.0ms (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	(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))))
0.7b	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_16269`
38×	`times-frac_binary64_16253`
37×	`*-un-lft-identity_binary64_16247` `add-cube-cbrt_binary64_16282`
36×	`associate-r_binary64_16187`
28×	`cube-prod_binary64_16275` `unpow-prod-down_binary64_16326`
17×	`add-exp-log_binary64_16285`
10×	`add-cbrt-cube_binary64_16283`
7×	`pow1_binary64_16308` `unswap-sqr_binary64_16215`
6×	`associate-l_binary64_16188`
5×	`prod-exp_binary64_16296`
4×	`add-log-exp_binary64_16286` `pow-exp_binary64_16315` `associate-*r/_binary64_16189` `cube-div_binary64_16276` `div-inv_binary64_16244`
3×	`sqr-pow_binary64_16219` `pow-unpow_binary64_16324`
2×	`cbrt-unprod_binary64_16280` `cube-mult_binary64_16277` `cbrt-prod_binary64_16278` `rem-cube-cbrt_binary64_16270` `unpow3_binary64_16313` `div-exp_binary64_16298` `*-commutative_binary64_16178` `pow-to-exp_binary64_16316` `cbrt-div_binary64_16279`
1×	`pow-prod-down_binary64_16318` `pow-pow_binary64_16319` `pow1/3_binary64_16329` `cbrt-undiv_binary64_16281`

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)

series567.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
131.0ms	(.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))))
114.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
111.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5112	2969

prune356.0ms (4.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	5	6	11
Picked	0	1	1
Done	0	1	1
Total	146	10	156

Merged error: 0b

Counts

156 → 10

Compiler

Compiled 5400 to 4278 computations (20.8% saved)

regimes23.0ms (0.3%)

Compiler: Compiled 184 to 160 computations (13% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample2.6s (35.7%)

Algorithm

1×

intervals

Results

1.2s	2015×	body	1024	valid
487.0ms	4424×	body	128	valid
347.0ms	1020×	body	512	valid
125.0ms	535×	body	256	valid
7.0ms	6×	body	2048	valid

Compiler

Compiled 233 to 204 computations (12.4% saved)

Details

analyze850.0ms (11.7%)

sample75.0ms (1%)

simplify187.0ms (2.6%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite28.0ms (0.4%)

series204.0ms (2.8%)

simplify85.0ms (1.2%)

prune465.0ms (6.4%)

localize10.0ms (0.1%)

rewrite31.0ms (0.4%)

series222.0ms (3.1%)

simplify71.0ms (1%)

prune417.0ms (5.7%)

localize12.0ms (0.2%)

rewrite53.0ms (0.7%)

series465.0ms (6.4%)

simplify80.0ms (1.1%)

prune312.0ms (4.3%)

localize13.0ms (0.2%)

rewrite53.0ms (0.7%)

series567.0ms (7.8%)

simplify64.0ms (0.9%)

prune356.0ms (4.9%)

regimes23.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (35.7%)

Profiling