Details

analyze1.1s (7.8%)

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)

sample71.0ms (0.5%)

Algorithm

1×

intervals

Results

38.0ms	119×	body	1024	valid
8.0ms	41×	body	512	valid
4.0ms	28×	body	256	valid
4.0ms	64×	body	128	valid
4.0ms	4×	body	2048	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify97.0ms (0.7%)

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

15.0b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

4.3b	(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))))
0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.3b	(cos.f64 (+.f64 a b))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_426`
19×	`times-frac_binary64_410` `*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
13×	`associate-r_binary64_344`
10×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
5×	`pow1_binary64_465`
3×	`associate-l_binary64_345` `associate-/r_binary64_348` `add-log-exp_binary64_443` `associate-/l_binary64_349`
2×	`div-exp_binary64_455` `div-inv_binary64_401` `unswap-sqr_binary64_372` `cbrt-undiv_binary64_438` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
1×	`pow-prod-down_binary64_475` `-commutative_binary64_335` `frac-2neg_binary64_415` `cos-sum_binary64_538` `associate-r/_binary64_346` `clear-num_binary64_403`

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

series494.0ms (3.6%)

Counts

3 → 36

Calls

3 calls:

290.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
159.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
44.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1006 to 759 computations (24.6% saved)

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5002	2050

prune135.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	12	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Error

0.2b

Counts

104 → 12

Compiler

Compiled 1922 to 552 computations (71.3% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_426`
22×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
20×	`associate-r_binary64_344`
19×	`times-frac_binary64_410`
13×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
8×	`pow1_binary64_465` `associate-/r/_binary64_350`
7×	`sin-mult_binary64_559`
6×	`associate-l_binary64_345` `cos-mult_binary64_558` `add-log-exp_binary64_443`
3×	`associate-/r_binary64_348` `unswap-sqr_binary64_372` `flip3--_binary64_408` `frac-sub_binary64_413` `associate-/l_binary64_349` `flip--_binary64_379` `sub-div_binary64_411` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
2×	`pow-prod-down_binary64_475` `div-exp_binary64_455` `*-commutative_binary64_335` `div-inv_binary64_401` `cbrt-undiv_binary64_438`
1×	`cancel-sign-sub-inv_binary64_370` `frac-2neg_binary64_415` `associate-*r/_binary64_346` `diff-log_binary64_496` `clear-num_binary64_403` `sub-neg_binary64_397`

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)))))
11.0ms	(/.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))

series1.2s (8.7%)

Counts

4 → 44

Calls

4 calls:

606.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
325.0ms	(/.f64 (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)))
91.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Compiler

Compiled 1488 to 1080 computations (27.4% saved)

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4980	3705
1	4980	3705

prune197.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	145	11	156

Error

0.0b

Counts

156 → 11

Compiler

Compiled 3712 to 846 computations (77.2% saved)

localize13.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.1b	(*.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)))
0.1b	(*.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))))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_426`
13×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
10×	`*-un-lft-identity_binary64_404` `add-cube-cbrt_binary64_439`
8×	`pow1_binary64_465`
6×	`associate-l_binary64_345` `associate-r_binary64_344` `add-log-exp_binary64_443`
5×	`sin-mult_binary64_559`
4×	`cos-mult_binary64_558` `associate-/r/_binary64_350`
3×	`associate-/r*_binary64_348` `times-frac_binary64_410` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
2×	`pow-prod-down_binary64_475` `div-exp_binary64_455` `*-commutative_binary64_335` `unswap-sqr_binary64_372` `flip3--_binary64_408` `frac-sub_binary64_413` `cbrt-undiv_binary64_438` `flip--_binary64_379` `sub-div_binary64_411`
1×	`cancel-sign-sub-inv_binary64_370` `frac-2neg_binary64_415` `div-inv_binary64_401` `diff-log_binary64_496` `clear-num_binary64_403` `sub-neg_binary64_397` `associate-/l*_binary64_349`

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))

series904.0ms (6.7%)

Counts

4 → 40

Calls

4 calls:

593.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
158.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
84.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
69.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1309 to 961 computations (26.6% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4978	2215
1	4978	2215

prune113.0ms (0.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	116	11	127

Error

0.0b

Counts

127 → 11

Compiler

Compiled 2691 to 612 computations (77.3% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

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

rewrite34.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_426`
29×	`*-un-lft-identity_binary64_404`
19×	`add-cube-cbrt_binary64_439`
18×	`times-frac_binary64_410`
13×	`add-cbrt-cube_binary64_440` `add-exp-log_binary64_442`
8×	`associate-/r*_binary64_348`
6×	`pow1_binary64_465` `add-log-exp_binary64_443`
5×	`distribute-lft-out--_binary64_356` `difference-of-squares_binary64_373`
4×	`associate-/l*_binary64_349`
3×	`div-exp_binary64_455` `cancel-sign-sub-inv_binary64_370` `associate-l_binary64_345` `associate-r_binary64_344` `cbrt-undiv_binary64_438`
2×	`frac-2neg_binary64_415` `cos-mult_binary64_558` `div-inv_binary64_401` `associate-/r/_binary64_350` `clear-num_binary64_403` `flip3--_binary64_408` `flip--_binary64_379` `prod-exp_binary64_453` `cbrt-unprod_binary64_437`
1×	`associate-/l/_binary64_351` `pow-prod-down_binary64_475` `*-commutative_binary64_335` `unswap-sqr_binary64_372` `diff-log_binary64_496` `sub-neg_binary64_397`

Counts

4 → 94

Calls

8 calls:

9.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
5.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
4.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series970.0ms (7.2%)

Counts

4 → 43

Calls

4 calls:

540.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
175.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
166.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
90.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

Compiler

Compiled 1231 to 954 computations (22.5% saved)

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	3042
1	4961	3042

prune122.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	138	10	148

Error

0.0b

Counts

148 → 10

Compiler

Compiled 2679 to 538 computations (79.9% saved)

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	521	2414
1	521	2414

regimes835.0ms (6.2%)

Accuracy

Total 0.3b remaining (95.5%)

Threshold costs 0.3b (95.5%)

Compiler

Compiled 7571 to 4835 computations (36.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample6.8s (50.4%)

Algorithm

1×

intervals

Results

1.1s	3613×	body	1024	valid
272.0ms	1284×	body	512	valid
167.0ms	2308×	body	128	valid
113.0ms	193×	body	2048	valid
85.0ms	602×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 4369 to 2778 computations (36.4% saved)

Pareto

0.3363416637847479

Details

analyze1.1s (7.8%)

sample71.0ms (0.5%)

simplify97.0ms (0.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite25.0ms (0.2%)

series494.0ms (3.6%)

simplify74.0ms (0.5%)

prune135.0ms (1%)

localize14.0ms (0.1%)

rewrite44.0ms (0.3%)

series1.2s (8.7%)

simplify96.0ms (0.7%)

prune197.0ms (1.5%)

localize13.0ms (0.1%)

rewrite29.0ms (0.2%)

series904.0ms (6.7%)

simplify66.0ms (0.5%)

prune113.0ms (0.8%)

localize12.0ms (0.1%)

rewrite34.0ms (0.3%)

series970.0ms (7.2%)

simplify86.0ms (0.6%)

prune122.0ms (0.9%)

simplify43.0ms (0.3%)

regimes835.0ms (6.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.8s (50.4%)

Profiling