Details

analyze1.1s (10.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	56
1	66	56
0	3	3
1	3	3

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)

sample68.0ms (0.7%)

Algorithm

1×

intervals

Results

30.0ms	106×	body	1024	valid
10.0ms	81×	body	128	valid
8.0ms	40×	body	512	valid
4.0ms	7×	body	2048	valid
3.0ms	22×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify7.0ms (0.1%)

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

14.4b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0b	(cos.f64 (+.f64 a b))

rewrite59.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `times-frac_binary64_425` `associate-/r_binary64_363` `associate-l_binary64_360` `associate-r*_binary64_359`
2×	`prod-exp_binary64_468` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `cbrt-unprod_binary64_452`
1×	`cos-sum_binary64_553` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `associate-/l_binary64_364` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350`

Counts

3 → 47

Calls

3 calls:

5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 725 to 158 computations (78.2% saved)

series390.0ms (3.8%)

Error

13.1b

Counts

3 → 30

Calls

3 calls:

263.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
61.0ms	(*.f64 r (sin.f64 b))
43.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1135 to 696 computations (38.7% saved)

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5006	1107

prune71.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	9	78

Error

0.2b

Counts

78 → 9

Compiler

Compiled 1167 to 340 computations (70.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite127.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 76

Calls

4 calls:

18.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
9.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
5.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
4.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1946 to 307 computations (84.2% saved)

series853.0ms (8.3%)

Error

0.2b

Counts

4 → 38

Calls

4 calls:

523.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
155.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
85.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
63.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1920 to 1065 computations (44.5% saved)

simplify66.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5090	2099

prune112.0ms (1.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Error

0.0b

Counts

123 → 11

Compiler

Compiled 2623 to 584 computations (77.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite115.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

31×	`add-sqr-sqrt_binary64_441`
29×	`*-un-lft-identity_binary64_419`
19×	`add-cube-cbrt_binary64_454`
18×	`times-frac_binary64_425`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`associate-/r*_binary64_363`
6×	`pow1_binary64_480` `add-log-exp_binary64_458`
5×	`difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371`
4×	`associate-/l*_binary64_364`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-l_binary64_360` `associate-r_binary64_359` `cancel-sign-sub-inv_binary64_385`
2×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `cos-mult_binary64_573` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip--_binary64_394`
1×	`associate-/l/_binary64_366` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `*-commutative_binary64_350` `diff-log_binary64_511` `sub-neg_binary64_412`

Counts

4 → 94

Calls

4 calls:

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

Compiler

Compiled 2167 to 410 computations (81.1% saved)

series914.0ms (8.9%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

477.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
172.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
157.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))
83.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 1685 to 1009 computations (40.1% saved)

simplify88.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4987	2879
1	4987	2879

prune118.0ms (1.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	131	13	144

Error

0.0b

Counts

144 → 13

Compiler

Compiled 2896 to 686 computations (76.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
0.3b	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
25.1b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

rewrite268.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`add-sqr-sqrt_binary64_441`
10×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
9×	`pow1_binary64_480`
8×	`cbrt-prod_binary64_450`
4×	`add-log-exp_binary64_458` `sin-mult_binary64_574`
3×	`cube-div_binary64_448` `pow-unpow_binary64_496` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `times-frac_binary64_425` `associate-/r/_binary64_365` `associate-/r_binary64_363` `associate-l_binary64_360` `associate-r*_binary64_359`
2×	`cbrt-div_binary64_451` `unpow-prod-down_binary64_498` `unpow3_binary64_485` `cube-mult_binary64_449` `cube-prod_binary64_447` `sqr-pow_binary64_391` `pow-prod-down_binary64_490` `pow-pow_binary64_491` `pow-exp_binary64_487` `rem-cube-cbrt_binary64_442` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`pow1/3_binary64_501` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `cos-mult_binary64_573` `frac-sub_binary64_428` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l_binary64_364` `unswap-sqr_binary64_387` `-commutative_binary64_350`

Counts

4 → 84

Calls

4 calls:

11.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (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))

Compiler

Compiled 2403 to 785 computations (67.3% saved)

series887.0ms (8.7%)

Error

0.0b

Counts

4 → 37

Calls

4 calls:

501.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))))
170.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
95.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
92.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

Compiler

Compiled 2181 to 1316 computations (39.7% saved)

simplify83.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4966	2080
1	4966	2080

prune99.0ms (1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	121	13	134

Error

0.0b

Counts

134 → 13

Compiler

Compiled 2711 to 731 computations (73% saved)

regimes777.0ms (7.6%)

Accuracy

Total 0.3b remaining (96.1%)

Threshold costs 0.3b (96.1%)

Compiler

Compiled 9334 to 5646 computations (39.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample3.9s (38.2%)

Algorithm

1×

intervals

Results

1.0s	3483×	body	1024	valid
274.0ms	1360×	body	512	valid
174.0ms	2369×	body	128	valid
135.0ms	206×	body	2048	valid
93.0ms	582×	body	256	valid
0.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 2326 to 1413 computations (39.3% saved)

Details

analyze1.1s (10.8%)

sample68.0ms (0.7%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite59.0ms (0.6%)

series390.0ms (3.8%)

simplify65.0ms (0.6%)

prune71.0ms (0.7%)

localize13.0ms (0.1%)

rewrite127.0ms (1.2%)

series853.0ms (8.3%)

simplify66.0ms (0.6%)

prune112.0ms (1.1%)

localize14.0ms (0.1%)

rewrite115.0ms (1.1%)

series914.0ms (8.9%)

simplify88.0ms (0.9%)

prune118.0ms (1.1%)

localize18.0ms (0.2%)

rewrite268.0ms (2.6%)

series887.0ms (8.7%)

simplify83.0ms (0.8%)

prune99.0ms (1%)

regimes777.0ms (7.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.9s (38.2%)

Profiling