Details

analyze1.0s (9.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample66.0ms (0.6%)

Algorithm

1×

intervals

Results

35.0ms	106×	body	1024	valid
10.0ms	52×	body	512	valid
5.0ms	71×	body	128	valid
3.0ms	23×	body	256	valid
2.0ms	4×	body	2048	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify88.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.2b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

3.0b	(cos.f64 (+.f64 a b))
0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
3.0b	(cos.f64 (+.f64 a b))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_441`
19×	`*-un-lft-identity_binary64_419` `times-frac_binary64_425` `add-cube-cbrt_binary64_454`
13×	`associate-r_binary64_359`
10×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `associate-l_binary64_360` `associate-/r_binary64_363` `associate-/l_binary64_364`
2×	`div-inv_binary64_416` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `cos-sum_binary64_553` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

3 → 67

Calls

6 calls:

8.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

series474.0ms (4.6%)

Counts

3 → 34

Calls

3 calls:

280.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
152.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
43.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1006 to 759 computations (24.6% saved)

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5116	1812

prune121.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Error

0.2b

Counts

102 → 9

Compiler

Compiled 1706 to 448 computations (73.7% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_441`
22×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
20×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`associate-/r/_binary64_365` `pow1_binary64_480`
7×	`sin-mult_binary64_574`
6×	`add-log-exp_binary64_458` `cos-mult_binary64_573` `associate-l_binary64_360`
3×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip3--_binary64_423` `flip--_binary64_394` `associate-/r_binary64_363` `sub-div_binary64_426` `frac-sub_binary64_428` `associate-/l_binary64_364`
2×	`pow-prod-down_binary64_490` `div-inv_binary64_416` `*-commutative_binary64_350` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `associate-*r/_binary64_361` `frac-2neg_binary64_430` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 100

Calls

8 calls:

12.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
8.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.1s (11.1%)

Counts

4 → 44

Calls

4 calls:

585.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
314.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
147.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
97.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Compiler

Compiled 1530 to 1110 computations (27.5% saved)

simplify96.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4966	3559
1	4966	3559

prune199.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	141	12	153

Error

0.0b

Counts

153 → 12

Compiler

Compiled 3643 to 821 computations (77.5% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(*.f64 r (sin.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(*.f64 r (sin.f64 b))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360`
5×	`sin-mult_binary64_574`
4×	`associate-/r/_binary64_365` `cos-mult_binary64_573`
3×	`times-frac_binary64_425` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-/r*_binary64_363`
2×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `flip3--_binary64_423` `*-commutative_binary64_350` `flip--_binary64_394` `sub-div_binary64_426` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `div-inv_binary64_416` `frac-2neg_binary64_430` `diff-log_binary64_511` `cancel-sign-sub-inv_binary64_385` `associate-/l*_binary64_364`

Counts

4 → 76

Calls

8 calls:

9.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 r (sin.f64 b))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series900.0ms (8.7%)

Counts

4 → 43

Calls

4 calls:

581.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
152.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
96.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
70.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1390 to 1021 computations (26.5% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5174	2227

prune109.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Error

0.0b

Counts

131 → 11

Compiler

Compiled 2743 to 641 computations (76.6% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3)))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.3b	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
26.9b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_441`
19×	`associate-r_binary64_359`
16×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
14×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
11×	`pow1_binary64_480`
10×	`times-frac_binary64_425`
8×	`cbrt-prod_binary64_450`
6×	`associate-l_binary64_360`
4×	`add-log-exp_binary64_458` `sin-mult_binary64_574` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
3×	`pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `cube-div_binary64_448` `associate-/r/_binary64_365` `pow-unpow_binary64_496`
2×	`unpow-prod-down_binary64_498` `cbrt-div_binary64_451` `unpow3_binary64_485` `cube-mult_binary64_449` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `sqr-pow_binary64_391` `*-commutative_binary64_350` `cube-prod_binary64_447` `pow-pow_binary64_491`
1×	`pow1/3_binary64_501` `div-inv_binary64_416` `flip3--_binary64_423` `associate-*r/_binary64_361` `rem-cbrt-cube_binary64_443` `cos-mult_binary64_573` `pow-to-exp_binary64_488` `flip--_binary64_394` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`

Counts

4 → 95

Calls

8 calls:

16.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
5.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series968.0ms (9.4%)

Counts

4 → 41

Calls

4 calls:

591.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)))))
187.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
96.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
93.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

Compiler

Compiled 1567 to 1173 computations (25.1% saved)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5034	2630

prune134.0ms (1.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	136	11	147

Error

0.0b

Counts

147 → 11

Compiler

Compiled 3333 to 973 computations (70.8% saved)

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	505	2419
1	505	2419

regimes387.0ms (3.8%)

Compiler: Compiled 4359 to 2592 computations (40.5% saved)

bsearch0.0ms (0%)

regimes156.0ms (1.5%)

Compiler: Compiled 1074 to 942 computations (12.3% saved)

bsearch0.0ms (0%)

regimes148.0ms (1.4%)

Compiler: Compiled 1026 to 906 computations (11.7% saved)

bsearch0.0ms (0%)

regimes106.0ms (1%)

Compiler: Compiled 657 to 633 computations (3.7% saved)

bsearch0.0ms (0%)

regimes102.0ms (1%)

Compiler: Compiled 618 to 600 computations (2.9% saved)

bsearch0.0ms (0%)

regimes87.0ms (0.8%)

Compiler: Compiled 114 to 153 computations (-34.2% saved)

bsearch79.0ms (0.8%)

Steps

Iters	Range		Point
9	4.7108576861351374e-21	1.2174788082581859e-15	1.2018833323933556e-15
10	-1.0323682737881521e-06	-9.629081624821127e-17	-1.0168394498600097e-06

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes76.0ms (0.7%)

Compiler: Compiled 72 to 111 computations (-54.2% saved)

bsearch83.0ms (0.8%)

Steps

Iters	Range		Point
10	5.607460290547805e-15	0.01370526432397266	2.328312582361087e-05
10	-2.783093503206085	-4.0863092004357396e-11	-5.187166954889571e-05

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes32.0ms (0.3%)

Compiler: Compiled 51 to 90 computations (-76.5% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

Accuracy

Total 0.3b remaining (94.5%)

Threshold costs 0.3b (94.5%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 132 to 100 computations (24.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	87	189
1	87	189

end0.0ms (0%)

sample3.3s (31.9%)

Algorithm

1×

intervals

Results

1.0s	3497×	body	1024	valid
258.0ms	1329×	body	512	valid
169.0ms	2339×	body	128	valid
115.0ms	209×	body	2048	valid
92.0ms	626×	body	256	valid
1.0ms	2×	body	1024	invalid
0.0ms	2×	body	512	invalid

Compiler

Compiled 1581 to 972 computations (38.5% saved)

Pareto

0.4443323324901527

Details

analyze1.0s (9.8%)

sample66.0ms (0.6%)

simplify88.0ms (0.8%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite25.0ms (0.2%)

series474.0ms (4.6%)

simplify71.0ms (0.7%)

prune121.0ms (1.2%)

localize13.0ms (0.1%)

rewrite43.0ms (0.4%)

series1.1s (11.1%)

simplify96.0ms (0.9%)

prune199.0ms (1.9%)

localize13.0ms (0.1%)

rewrite31.0ms (0.3%)

series900.0ms (8.7%)

simplify66.0ms (0.6%)

prune109.0ms (1.1%)

localize16.0ms (0.2%)

rewrite38.0ms (0.4%)

series968.0ms (9.4%)

simplify70.0ms (0.7%)

prune134.0ms (1.3%)

simplify33.0ms (0.3%)

regimes387.0ms (3.8%)

bsearch0.0ms (0%)

regimes156.0ms (1.5%)

bsearch0.0ms (0%)

regimes148.0ms (1.4%)

bsearch0.0ms (0%)

regimes106.0ms (1%)

bsearch0.0ms (0%)

regimes102.0ms (1%)

bsearch0.0ms (0%)

regimes87.0ms (0.8%)

bsearch79.0ms (0.8%)

regimes76.0ms (0.7%)

bsearch83.0ms (0.8%)

regimes32.0ms (0.3%)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

bsearch8.0ms (0.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.3s (31.9%)

Profiling