Details

analyze1.0s (18.5%)

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)

sample137.0ms (2.5%)

Algorithm

1×

intervals

Results

73.0ms	62×	body	1280	valid
27.0ms	45×	body	640	valid
18.0ms	126×	body	80	valid
7.0ms	15×	body	320	valid
3.0ms	8×	body	160	valid

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	50	22
1	50	22

prune4.0ms (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: 13.2b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize10.0ms (0.2%)

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)))
12.9b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite39.0ms (0.7%)

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:

15.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
11.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
11.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series24.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

13.0ms	(/.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))))
4.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

simplify117.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4947	1066
1	4947	1066

prune106.0ms (1.9%)

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 1372 to 1046 computations (23.8% saved)

localize9.0ms (0.2%)

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

rewrite23.0ms (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:

9.0ms	(.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)

series27.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

14.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
9.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
4.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

simplify124.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4905	1245
1	4905	1245

prune85.0ms (1.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	74	14	88

Merged error: 0.0b

Counts

88 → 14

Compiler

Compiled 1611 to 1211 computations (24.8% 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 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
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)))

rewrite44.0ms (0.8%)

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)))
12.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
9.0ms	(.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))

series50.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(.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)))
16.0ms	(/.f64 (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3)) (sin.f64 x))
9.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) (sqrt.f64 8/3)) (sqrt.f64 8/3))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (sqrt.f64 8/3))

simplify115.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4909	1753
1	4909	1753

prune115.0ms (2.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	10	12
Picked	0	1	1
Done	1	0	1
Total	108	13	121

Merged error: 0.0b

Counts

121 → 13

Compiler

Compiled 2347 to 1831 computations (22% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (sin.f64 x))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (/.f64 1 (sin.f64 x))))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)
0.4b	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (/.f64 1 (sin.f64 x)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

64×	`add-exp-log_binary64`
38×	`add-cbrt-cube_binary64`
34×	`prod-exp_binary64`
24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`pow1_binary64`
18×	`cbrt-unprod_binary64` `times-frac_binary64`
17×	`associate-r_binary64`
10×	`pow-prod-down_binary64` `div-exp_binary64`
7×	`associate-l_binary64`
5×	`1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `*-commutative_binary64`
2×	`un-div-inv_binary64` `div-inv_binary64`
1×	`unswap-sqr_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 118

Calls

4 calls:

13.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (/.f64 1 (sin.f64 x))))
11.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (/.f64 1 (sin.f64 x)))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)
4.0ms	(/.f64 1 (sin.f64 x))

series34.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 (.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (/.f64 1 (sin.f64 x))))
12.0ms	(.f64 (.f64 (sin.f64 (*.f64 x 1/2)) 8/3) (/.f64 1 (sin.f64 x)))
4.0ms	(/.f64 1 (sin.f64 x))
4.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

simplify106.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4978	1883
1	4978	1883

prune100.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	130	13	143

Merged error: 0.0b

Counts

143 → 13

Compiler

Compiled 2406 to 1785 computations (25.8% saved)

regimes39.0ms (0.7%)

Compiler: Compiled 266 to 231 computations (13.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample3.1s (56.2%)

Algorithm

1×

intervals

Results

1.1s	1544×	body	1280	valid
569.0ms	1304×	body	640	valid
428.0ms	4242×	body	80	valid
188.0ms	611×	body	320	valid
61.0ms	299×	body	160	valid

Compiler

Compiled 315 to 275 computations (12.7% saved)

Details

analyze1.0s (18.5%)

sample137.0ms (2.5%)

simplify15.0ms (0.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite39.0ms (0.7%)

series24.0ms (0.4%)

simplify117.0ms (2.1%)

prune106.0ms (1.9%)

localize9.0ms (0.2%)

rewrite23.0ms (0.4%)

series27.0ms (0.5%)

simplify124.0ms (2.3%)

prune85.0ms (1.6%)

localize12.0ms (0.2%)

rewrite44.0ms (0.8%)

series50.0ms (0.9%)

simplify115.0ms (2.1%)

prune115.0ms (2.1%)

localize11.0ms (0.2%)

rewrite37.0ms (0.7%)

series34.0ms (0.6%)

simplify106.0ms (1.9%)

prune100.0ms (1.8%)

regimes39.0ms (0.7%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.1s (56.2%)

Profiling