Details

analyze1.2s (7.5%)

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)

sample66.0ms (0.4%)

Algorithm

1×

intervals

Results

35.0ms	120×	body	1024	valid
7.0ms	37×	body	512	valid
5.0ms	74×	body	128	valid
3.0ms	6×	body	2048	valid
3.0ms	19×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune3.0ms (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

16.8b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite83.0ms (0.5%)

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

Compiler

Compiled 703 to 152 computations (78.4% saved)

series659.0ms (4.2%)

Error

14.7b

Counts

3 → 35

Calls

3 calls:

447.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
106.0ms	(*.f64 r (sin.f64 b))
61.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1348 to 894 computations (33.7% saved)

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4943	1413
1	4943	1413

prune127.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Error

0.2b

Counts

83 → 10

Compiler

Compiled 1278 to 492 computations (61.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite180.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-sqr-sqrt_binary64_441`
15×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
10×	`pow1_binary64_480`
9×	`associate-l_binary64_360` `associate-r_binary64_359`
4×	`prod-exp_binary64_468` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365`
3×	`sin-mult_binary64_574` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350` `times-frac_binary64_425` `cos-mult_binary64_573` `associate-/r_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `frac-sub_binary64_428` `sub-div_binary64_426` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 81

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
7.0ms	(*.f64 r (sin.f64 b))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
4.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 1859 to 324 computations (82.6% saved)

series1.4s (9.1%)

Error

0.2b

Counts

4 → 44

Calls

4 calls:

945.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
156.0ms	(*.f64 (cos.f64 b) (cos.f64 a))
153.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
112.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 2198 to 1365 computations (37.9% saved)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4958	2280
1	4958	2280

prune202.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	14	125
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	121	14	135

Error

0.0b

Counts

135 → 14

Compiler

Compiled 2514 to 767 computations (69.5% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite187.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

18×	`add-sqr-sqrt_binary64_441`
15×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
12×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
10×	`pow1_binary64_480`
9×	`associate-l_binary64_360` `associate-r_binary64_359`
4×	`prod-exp_binary64_468` `add-log-exp_binary64_458` `cbrt-unprod_binary64_452` `associate-/r/_binary64_365`
3×	`sin-mult_binary64_574` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `-commutative_binary64_350` `times-frac_binary64_425` `cos-mult_binary64_573` `associate-/r_binary64_363`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `frac-sub_binary64_428` `sub-div_binary64_426` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l*_binary64_364`

Counts

4 → 81

Calls

4 calls:

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

Compiler

Compiled 1859 to 328 computations (82.4% saved)

series1.4s (9%)

Error

0.0b

Counts

4 → 44

Calls

4 calls:

947.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a))))
152.0ms	(*.f64 (cos.f64 a) (cos.f64 b))
136.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
116.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 2230 to 1370 computations (38.6% saved)

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5005	2312

prune213.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	8	5	13
Picked	0	1	1
Done	0	0	0
Total	127	12	139

Error

0.0b

Counts

139 → 12

Compiler

Compiled 2474 to 736 computations (70.3% saved)

localize15.0ms (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))

rewrite201.0ms (1.3%)

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))
4.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 2034 to 382 computations (81.2% saved)

series1.7s (10.5%)

Error

0.0b

Counts

4 → 50

Calls

4 calls:

879.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
274.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
274.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))
163.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 2101 to 1395 computations (33.6% saved)

simplify111.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4960	3420
1	4960	3420

prune207.0ms (1.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	145	11	156

Error

0.0b

Counts

156 → 11

Compiler

Compiled 2395 to 651 computations (72.8% saved)

regimes5.0s (31.4%)

Accuracy

Total 0.3b remaining (83.3%)

Threshold costs 0.3b (83.3%)

Compiler

Compiled 46537 to 30938 computations (33.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	26
1	44	26

end2.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample2.6s (16.3%)

Algorithm

1×

intervals

Results

1.3s	3565×	body	1024	valid
281.0ms	1355×	body	512	valid
168.0ms	2316×	body	128	valid
117.0ms	202×	body	2048	valid
82.0ms	562×	body	256	valid
1.0ms	2×	body	1024	invalid
0.0ms	1×	body	128	invalid

Compiler

Compiled 261 to 202 computations (22.6% saved)

Details

analyze1.2s (7.5%)

sample66.0ms (0.4%)

simplify12.0ms (0.1%)

prune3.0ms (0%)

localize9.0ms (0.1%)

rewrite83.0ms (0.5%)

series659.0ms (4.2%)

simplify87.0ms (0.5%)

prune127.0ms (0.8%)

localize14.0ms (0.1%)

rewrite180.0ms (1.1%)

series1.4s (9.1%)

simplify67.0ms (0.4%)

prune202.0ms (1.3%)

localize14.0ms (0.1%)

rewrite187.0ms (1.2%)

series1.4s (9%)

simplify66.0ms (0.4%)

prune213.0ms (1.4%)

localize15.0ms (0.1%)

rewrite201.0ms (1.3%)

series1.7s (10.5%)

simplify111.0ms (0.7%)

prune207.0ms (1.3%)

regimes5.0s (31.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end2.0ms (0%)

sample2.6s (16.3%)

Profiling