Details

analyze1.3s (17.1%)

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)

sample71.0ms (1%)

Algorithm

1×

intervals

Results

33.0ms	61×	body	1024	valid
17.0ms	152×	body	128	valid
10.0ms	30×	body	512	valid
3.0ms	13×	body	256	valid

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify93.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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: 16.1b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize9.0ms (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)))
16.0b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64_13072` `add-exp-log_binary64_13074`
10×	`add-sqr-sqrt_binary64_13058` `pow1_binary64_13097`
8×	`*-un-lft-identity_binary64_13036` `add-cube-cbrt_binary64_13071`
7×	`prod-exp_binary64_13085` `cbrt-unprod_binary64_13069`
6×	`associate-l_binary64_12977`
4×	`associate-r_binary64_12976` `pow-prod-down_binary64_13107`
3×	`cbrt-undiv_binary64_13070` `add-log-exp_binary64_13075` `div-exp_binary64_13087` `associate-/r*_binary64_12980` `times-frac_binary64_13042`
2×	`*-commutative_binary64_12967`
1×	`clear-num_binary64_13035` `unswap-sqr_binary64_13004` `div-inv_binary64_13033` `associate-/l*_binary64_12981` `frac-2neg_binary64_13047`

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))
8.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))

series132.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

79.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
37.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
17.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

simplify107.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4934	1066
1	4934	1066

prune123.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	57	11	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	11	69

Merged error: 0.1b

Counts

69 → 11

Compiler

Compiled 1320 to 1009 computations (23.6% saved)

localize9.0ms (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)))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64_13072` `add-exp-log_binary64_13074`
14×	`add-sqr-sqrt_binary64_13058`
10×	`associate-r_binary64_12976` `*-un-lft-identity_binary64_13036` `add-cube-cbrt_binary64_13071`
7×	`pow1_binary64_13097`
6×	`associate-l_binary64_12977` `prod-exp_binary64_13085` `times-frac_binary64_13042` `cbrt-unprod_binary64_13069`
4×	`cbrt-undiv_binary64_13070` `div-exp_binary64_13087`
3×	`add-log-exp_binary64_13075` `associate-/r*_binary64_12980`
2×	`unswap-sqr_binary64_13004` `div-inv_binary64_13033` `*-commutative_binary64_12967` `pow-prod-down_binary64_13107`
1×	`clear-num_binary64_13035` `associate-/l_binary64_12981` `associate-r/_binary64_12978` `frac-2neg_binary64_13047`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
5.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

series163.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

84.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
45.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
34.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

simplify67.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4958	1245
1	4958	1245

prune113.0ms (1.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	73	13	86

Merged error: 0.0b

Counts

86 → 13

Compiler

Compiled 1573 to 1180 computations (25% saved)

localize11.0ms (0.1%)

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)))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_13058`
38×	`times-frac_binary64_13042`
37×	`*-un-lft-identity_binary64_13036` `add-cube-cbrt_binary64_13071`
36×	`associate-r_binary64_12976`
28×	`cube-prod_binary64_13064` `unpow-prod-down_binary64_13115`
17×	`add-exp-log_binary64_13074`
10×	`add-cbrt-cube_binary64_13072`
7×	`unswap-sqr_binary64_13004` `pow1_binary64_13097`
6×	`associate-l_binary64_12977`
5×	`prod-exp_binary64_13085`
4×	`add-log-exp_binary64_13075` `pow-exp_binary64_13104` `div-inv_binary64_13033` `cube-div_binary64_13065` `associate-*r/_binary64_12978`
3×	`pow-unpow_binary64_13113` `sqr-pow_binary64_13008`
2×	`unpow3_binary64_13102` `div-exp_binary64_13087` `cube-mult_binary64_13066` `cbrt-div_binary64_13068` `pow-to-exp_binary64_13105` `rem-cube-cbrt_binary64_13059` `cbrt-prod_binary64_13067` `*-commutative_binary64_12967` `cbrt-unprod_binary64_13069`
1×	`cbrt-undiv_binary64_13070` `pow-pow_binary64_13108` `pow1/3_binary64_13118` `pow-prod-down_binary64_13107`

Counts

4 → 131

Calls

4 calls:

18.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
9.0ms	(.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	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))
5.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)

series324.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
71.0ms	(.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))))
69.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))
69.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)

simplify59.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5124	2969

prune268.0ms (3.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	141	2	143
Fresh	4	7	11
Picked	0	1	1
Done	1	0	1
Total	146	10	156

Merged error: 0b

Counts

156 → 10

Compiler

Compiled 3580 to 2725 computations (23.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.9b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0b	(cbrt.f64 512/27)

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_13058`
39×	`cbrt-prod_binary64_13067`
38×	`*-un-lft-identity_binary64_13036` `add-cube-cbrt_binary64_13071`
36×	`times-frac_binary64_13042`
26×	`cube-prod_binary64_13064` `unpow-prod-down_binary64_13115`
9×	`add-exp-log_binary64_13074`
8×	`add-cbrt-cube_binary64_13072`
7×	`pow1_binary64_13097`
6×	`associate-r_binary64_12976`
4×	`add-log-exp_binary64_13075` `div-inv_binary64_13033`
3×	`associate-l_binary64_12977` `pow-unpow_binary64_13113`
2×	`unswap-sqr_binary64_13004` `unpow3_binary64_13102` `pow-exp_binary64_13104` `cube-mult_binary64_13066` `pow1/3_binary64_13118` `cube-div_binary64_13065` `rem-cube-cbrt_binary64_13059` `sqr-pow_binary64_13008`
1×	`cbrt-undiv_binary64_13070` `pow-pow_binary64_13108` `div-exp_binary64_13087` `rem-cbrt-cube_binary64_13060` `prod-exp_binary64_13085` `cbrt-div_binary64_13068` `pow-to-exp_binary64_13105` `*-commutative_binary64_12967` `pow-prod-down_binary64_13107` `cbrt-unprod_binary64_13069`

Counts

4 → 121

Calls

4 calls:

6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
5.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0ms	(cbrt.f64 512/27)

series140.0ms (1.9%)

Counts

4 → 10

Calls

4 calls:

68.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
40.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
31.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
0.0ms	(cbrt.f64 512/27)

simplify109.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5536	2404

prune217.0ms (3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	131	10	141

Merged error: 0b

Counts

141 → 10

Compiler

Compiled 3082 to 2352 computations (23.7% saved)

regimes237.0ms (3.2%)

Compiler: Compiled 1802 to 1542 computations (14.4% 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%)

sample3.7s (50.1%)

Algorithm

1×

intervals

Results

1.1s	2018×	body	1024	valid
591.0ms	4491×	body	128	valid
384.0ms	1013×	body	512	valid
126.0ms	469×	body	256	valid
9.0ms	9×	body	2048	valid

Compiler

Compiled 935 to 802 computations (14.2% saved)

Details

analyze1.3s (17.1%)

sample71.0ms (1%)

simplify93.0ms (1.3%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite29.0ms (0.4%)

series132.0ms (1.8%)

simplify107.0ms (1.5%)

prune123.0ms (1.7%)

localize9.0ms (0.1%)

rewrite23.0ms (0.3%)

series163.0ms (2.2%)

simplify67.0ms (0.9%)

prune113.0ms (1.5%)

localize11.0ms (0.1%)

rewrite51.0ms (0.7%)

series324.0ms (4.4%)

simplify59.0ms (0.8%)

prune268.0ms (3.7%)

localize12.0ms (0.2%)

rewrite28.0ms (0.4%)

series140.0ms (1.9%)

simplify109.0ms (1.5%)

prune217.0ms (3%)

regimes237.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.7s (50.1%)

Profiling