Details

analyze812.0ms (11.4%)

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)

sample67.0ms (0.9%)

Algorithm

1×

intervals

Results

29.0ms	71×	body	1024	valid
14.0ms	142×	body	128	valid
12.0ms	28×	body	512	valid
3.0ms	15×	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

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

Error

13.7b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize14.0ms (0.2%)

Local error

Found 6 expressions with local error:

13.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
0.4b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
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)))
13.5b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166`
10×	`add-sqr-sqrt_binary64_17150` `pow1_binary64_17189`
8×	`add-cube-cbrt_binary64_17163` `*-un-lft-identity_binary64_17128`
7×	`cbrt-unprod_binary64_17161` `prod-exp_binary64_17177`
6×	`associate-l_binary64_17069`
4×	`associate-r_binary64_17068` `pow-prod-down_binary64_17199`
3×	`cbrt-undiv_binary64_17162` `times-frac_binary64_17134` `add-log-exp_binary64_17167` `associate-/r*_binary64_17072` `div-exp_binary64_17179`
2×	`*-commutative_binary64_17059`
1×	`clear-num_binary64_17127` `associate-/l*_binary64_17073` `frac-2neg_binary64_17139` `unswap-sqr_binary64_17096` `div-inv_binary64_17125`

Counts

3 → 59

Calls

6 calls:

8.0ms	(/.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)))
0.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
0.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

series156.0ms (2.2%)

Counts

3 → 15

Calls

3 calls:

77.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
50.0ms	(.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)))

Compiler

Compiled 340 to 294 computations (13.5% saved)

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4934	1123
1	4934	1123

prune136.0ms (1.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	61	13	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	13	75

Error

0.1b

Counts

75 → 13

Compiler

Compiled 1466 to 1120 computations (23.6% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

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

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary64_17164` `add-exp-log_binary64_17166`
14×	`add-sqr-sqrt_binary64_17150`
10×	`add-cube-cbrt_binary64_17163` `associate-r_binary64_17068` `*-un-lft-identity_binary64_17128`
7×	`pow1_binary64_17189`
6×	`cbrt-unprod_binary64_17161` `prod-exp_binary64_17177` `times-frac_binary64_17134` `associate-l_binary64_17069`
4×	`cbrt-undiv_binary64_17162` `div-exp_binary64_17179`
3×	`add-log-exp_binary64_17167` `associate-/r*_binary64_17072`
2×	`unswap-sqr_binary64_17096` `*-commutative_binary64_17059` `pow-prod-down_binary64_17199` `div-inv_binary64_17125`
1×	`associate-r/_binary64_17070` `clear-num_binary64_17127` `associate-/l_binary64_17073` `frac-2neg_binary64_17139`

Counts

3 → 66

Calls

6 calls:

9.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)
5.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
0.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
0.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))

series159.0ms (2.2%)

Counts

3 → 15

Calls

3 calls:

77.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
51.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
31.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

Compiler

Compiled 344 to 298 computations (13.4% saved)

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4958	1290
1	4958	1290

prune126.0ms (1.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	80	14	94

Error

0.0b

Counts

94 → 14

Compiler

Compiled 1702 to 1282 computations (24.7% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_17150`
38×	`times-frac_binary64_17134`
37×	`add-cube-cbrt_binary64_17163` `*-un-lft-identity_binary64_17128`
36×	`associate-r_binary64_17068`
28×	`unpow-prod-down_binary64_17207` `cube-prod_binary64_17156`
17×	`add-exp-log_binary64_17166`
10×	`add-cbrt-cube_binary64_17164`
7×	`pow1_binary64_17189` `unswap-sqr_binary64_17096`
6×	`associate-l_binary64_17069`
5×	`prod-exp_binary64_17177`
4×	`associate-*r/_binary64_17070` `add-log-exp_binary64_17167` `cube-div_binary64_17157` `pow-exp_binary64_17196` `div-inv_binary64_17125`
3×	`pow-unpow_binary64_17205` `sqr-pow_binary64_17100`
2×	`cbrt-unprod_binary64_17161` `cbrt-prod_binary64_17159` `cbrt-div_binary64_17160` `unpow3_binary64_17194` `div-exp_binary64_17179` `*-commutative_binary64_17059` `cube-mult_binary64_17158` `pow-to-exp_binary64_17197` `rem-cube-cbrt_binary64_17151`
1×	`pow1/3_binary64_17210` `cbrt-undiv_binary64_17162` `pow-pow_binary64_17200` `pow-prod-down_binary64_17199`

Counts

4 → 131

Calls

8 calls:

14.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
8.0ms	(.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))))
7.0ms	(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)
0.0ms	(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))

series379.0ms (5.3%)

Counts

4 → 20

Calls

4 calls:

131.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
91.0ms	(.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))))
82.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
74.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

Compiler

Compiled 564 to 512 computations (9.2% saved)

simplify62.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5125	3039

prune234.0ms (3.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	4	8	12
Picked	0	1	1
Done	0	1	1
Total	153	12	165

Error

Counts

165 → 12

Compiler

Compiled 3721 to 2838 computations (23.7% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.4b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
0.2b	(/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x))
0.2b	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27)) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))
0.4b	(.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)
0.8b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0b	(cbrt.f64 512/27)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_17150`
39×	`cbrt-prod_binary64_17159`
38×	`add-cube-cbrt_binary64_17163` `*-un-lft-identity_binary64_17128`
36×	`times-frac_binary64_17134`
26×	`unpow-prod-down_binary64_17207` `cube-prod_binary64_17156`
9×	`add-exp-log_binary64_17166`
8×	`add-cbrt-cube_binary64_17164`
7×	`pow1_binary64_17189`
6×	`associate-r_binary64_17068`
4×	`add-log-exp_binary64_17167` `div-inv_binary64_17125`
3×	`pow-unpow_binary64_17205` `associate-l_binary64_17069`
2×	`pow1/3_binary64_17210` `sqr-pow_binary64_17100` `unswap-sqr_binary64_17096` `unpow3_binary64_17194` `cube-div_binary64_17157` `cube-mult_binary64_17158` `pow-exp_binary64_17196` `rem-cube-cbrt_binary64_17151`
1×	`cbrt-undiv_binary64_17162` `cbrt-unprod_binary64_17161` `prod-exp_binary64_17177` `pow-pow_binary64_17200` `cbrt-div_binary64_17160` `div-exp_binary64_17179` `*-commutative_binary64_17059` `rem-cbrt-cube_binary64_17152` `pow-prod-down_binary64_17199` `pow-to-exp_binary64_17197`

Counts

4 → 121

Calls

8 calls:

8.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
6.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0ms	(cbrt.f64 512/27)
0.0ms	(.f64 (.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27)) (cbrt.f64 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

series173.0ms (2.4%)

Counts

4 → 15

Calls

4 calls:

81.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
48.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
43.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
0.0ms	(cbrt.f64 512/27)

Compiler

Compiled 482 to 432 computations (10.4% saved)

simplify81.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5539	2442

prune191.0ms (2.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	136	12	148

Error

Counts

148 → 12

Compiler

Compiled 3154 to 2409 computations (23.6% saved)

simplify28.0ms (0.4%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	294	1765
1	294	1765

regimes122.0ms (1.7%)

Compiler: Compiled 1075 to 931 computations (13.4% saved)

bsearch0.0ms (0%)

regimes64.0ms (0.9%)

Compiler: Compiled 448 to 403 computations (10% saved)

bsearch0.0ms (0%)

regimes48.0ms (0.7%)

Compiler: Compiled 147 to 137 computations (6.8% saved)

bsearch58.0ms (0.8%)

Steps

Iters	Range		Point
9	5.137752320814203e-77	7.69710988166438e-72	5.195819335128253e-77
9	-7.56954319430061e-07	-9.889941251263232e-16	-1.428402078863971e-08

Compiler

Compiled 1 to 1 computations (0% saved)

regimes42.0ms (0.6%)

Compiler: Compiled 98 to 92 computations (6.1% saved)

bsearch61.0ms (0.9%)

Steps

Iters	Range		Point
9	4.088275092156049e-09	0.0004954605509814336	2.1261961902696117e-08
9	-7.56954319430061e-07	-9.889941251263232e-16	-1.428402078863971e-08

Compiler

Compiled 1 to 1 computations (0% saved)

regimes21.0ms (0.3%)

Compiler: Compiled 76 to 72 computations (5.3% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.2%)

Compiler: Compiled 66 to 62 computations (6.1% saved)

bsearch0.0ms (0%)

regimes27.0ms (0.4%)

Compiler: Compiled 31 to 31 computations (0% saved)

bsearch57.0ms (0.8%)

Steps

Iters	Range		Point
9	0.002189571073769023	681549.2647320819	176441.5486995892
9	-88.20697375801977	-2.2918986798597923e-05	-3.142896776850945

Compiler

Compiled 1 to 1 computations (0% saved)

regimes27.0ms (0.4%)

Compiler: Compiled 22 to 23 computations (-4.5% saved)

bsearch45.0ms (0.6%)

Steps

Iters	Range		Point
5	5.416142932655099e+17	1.102760176167425e+18	6.278287786841239e+17
9	-88.20697375801977	-2.2918986798597923e-05	-3.142896776850945

Compiler

Compiled 1 to 1 computations (0% saved)

regimes8.0ms (0.1%)

Compiler: Compiled 5 to 8 computations (-60% saved)

bsearch0.0ms (0%)

regimes7.0ms (0.1%)

Accuracy

Total 0.5b remaining (99.8%)

Threshold costs 0.5b (99.8%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch11.0ms (0.2%)

Compiler: Compiled 165 to 144 computations (12.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	237
1	83	237

end0.0ms (0%)

sample3.4s (48.3%)

Algorithm

1×

intervals

Results

874.0ms	2021×	body	1024	valid
449.0ms	4445×	body	128	valid
299.0ms	1057×	body	512	valid
104.0ms	469×	body	256	valid
6.0ms	8×	body	2048	valid

Compiler

Compiled 1261 to 1096 computations (13.1% saved)

Pareto

0.3996670016846209

Details

analyze812.0ms (11.4%)

sample67.0ms (0.9%)

simplify93.0ms (1.3%)

prune6.0ms (0.1%)

localize14.0ms (0.2%)

rewrite25.0ms (0.3%)

series156.0ms (2.2%)

simplify91.0ms (1.3%)

prune136.0ms (1.9%)

localize9.0ms (0.1%)

rewrite27.0ms (0.4%)

series159.0ms (2.2%)

simplify76.0ms (1.1%)

prune126.0ms (1.8%)

localize13.0ms (0.2%)

rewrite49.0ms (0.7%)

series379.0ms (5.3%)

simplify62.0ms (0.9%)

prune234.0ms (3.3%)

localize14.0ms (0.2%)

rewrite34.0ms (0.5%)

series173.0ms (2.4%)

simplify81.0ms (1.1%)

prune191.0ms (2.7%)

simplify28.0ms (0.4%)

regimes122.0ms (1.7%)

bsearch0.0ms (0%)

regimes64.0ms (0.9%)

bsearch0.0ms (0%)

regimes48.0ms (0.7%)

bsearch58.0ms (0.8%)

regimes42.0ms (0.6%)

bsearch61.0ms (0.9%)

regimes21.0ms (0.3%)

bsearch0.0ms (0%)

regimes17.0ms (0.2%)

bsearch0.0ms (0%)

regimes27.0ms (0.4%)

bsearch57.0ms (0.8%)

regimes27.0ms (0.4%)

bsearch45.0ms (0.6%)

regimes8.0ms (0.1%)

bsearch0.0ms (0%)

regimes7.0ms (0.1%)

bsearch11.0ms (0.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.4s (48.3%)

Profiling