Details

analyze1.4s (10.1%)

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)

sample80.0ms (0.6%)

Algorithm

1×

intervals

Results

43.0ms	106×	body	1024	valid
12.0ms	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)

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

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

14.2b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(*.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))

rewrite70.0ms (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:

6.0ms	(*.f64 r (sin.f64 b))
5.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 725 to 158 computations (78.2% saved)

series494.0ms (3.6%)

Error

13.2b

Counts

3 → 33

Calls

3 calls:

333.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
80.0ms	(*.f64 r (sin.f64 b))
45.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1310 to 802 computations (38.8% saved)

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4937	1166
1	4937	1166

prune99.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	8	81

Error

0.2b

Counts

81 → 8

Compiler

Compiled 1207 to 353 computations (70.8% 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)))
0.2b	(*.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))))

rewrite138.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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:

10.0ms	(/.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))
9.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
8.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 1946 to 307 computations (84.2% saved)

series1.3s (9.6%)

Error

0.2b

Counts

4 → 43

Calls

4 calls:

856.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
182.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
148.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
92.0ms	(*.f64 r (sin.f64 b))

Compiler

Compiled 2233 to 1240 computations (44.5% saved)

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4954	2225
1	4954	2225

prune179.0ms (1.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	12	119
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	115	12	127

Error

0.1b

Counts

127 → 12

Compiler

Compiled 2751 to 651 computations (76.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite167.0ms (1.2%)

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` `cancel-sign-sub-inv_binary64_385` `associate-l_binary64_360` `associate-r_binary64_359`
2×	`frac-2neg_binary64_430` `clear-num_binary64_418` `div-inv_binary64_416` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip--_binary64_394` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `cos-mult_binary64_573`
1×	`associate-/l/_binary64_366` `diff-log_binary64_511` `sub-neg_binary64_412` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `*-commutative_binary64_350`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(*.f64 (cos.f64 b) (cos.f64 a))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
6.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))

Compiler

Compiled 2167 to 410 computations (81.1% saved)

series1.1s (8.4%)

Error

0.1b

Counts

4 → 44

Calls

4 calls:

580.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a)))
234.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b)) (sin.f64 a))
171.0ms	(/.f64 (*.f64 (cos.f64 b) (cos.f64 a)) (sin.f64 b))
129.0ms	(*.f64 (cos.f64 b) (cos.f64 a))

Compiler

Compiled 1962 to 1171 computations (40.3% saved)

simplify127.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4968	3003
1	4968	3003

prune158.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	138	12	150

Error

0.0b

Counts

150 → 12

Compiler

Compiled 2966 to 724 computations (75.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a))
0.2b	(/.f64 (sin.f64 b) (cos.f64 a))
0.2b	(/.f64 r (-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a)))
0.3b	(/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a)))

rewrite209.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

120×	`times-frac_binary64_425`
112×	`add-sqr-sqrt_binary64_441`
77×	`*-un-lft-identity_binary64_419`
67×	`add-cube-cbrt_binary64_454`
23×	`associate-/r*_binary64_363`
15×	`difference-of-squares_binary64_388`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`associate-/l*_binary64_364`
7×	`div-inv_binary64_416`
6×	`add-log-exp_binary64_458`
5×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `distribute-lft-out--_binary64_371`
4×	`pow1_binary64_480`
3×	`frac-2neg_binary64_430` `clear-num_binary64_418` `associate-/r/_binary64_365` `cancel-sign-sub-inv_binary64_385`
2×	`flip3--_binary64_423` `flip--_binary64_394`
1×	`diff-log_binary64_511` `sub-neg_binary64_412`

Counts

4 → 160

Calls

4 calls:

23.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a)))
20.0ms	(-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a))
7.0ms	(/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a)))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 a))

Compiler

Compiled 4003 to 778 computations (80.6% saved)

series1.3s (9.3%)

Error

0.0b

Counts

4 → 46

Calls

4 calls:

639.0ms	(/.f64 r (-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a)))
227.0ms	(-.f64 (/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a))) (sin.f64 a))
215.0ms	(/.f64 (cos.f64 b) (/.f64 (sin.f64 b) (cos.f64 a)))
151.0ms	(/.f64 (sin.f64 b) (cos.f64 a))

Compiler

Compiled 2080 to 1243 computations (40.2% saved)

simplify115.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4956	5289
1	4956	5289

prune182.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	206	12	218

Error

0.0b

Counts

218 → 12

Compiler

Compiled 4500 to 863 computations (80.8% saved)

regimes1.2s (8.5%)

Accuracy

Total 0.3b remaining (96.1%)

Threshold costs 0.3b (96.1%)

Compiler

Compiled 10784 to 6487 computations (39.8% 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%)

sample5.1s (37.4%)

Algorithm

1×

intervals

Results

1.3s	3497×	body	1024	valid
325.0ms	1329×	body	512	valid
195.0ms	2339×	body	128	valid
138.0ms	209×	body	2048	valid
110.0ms	626×	body	256	valid
1.0ms	2×	body	1024	invalid
0.0ms	2×	body	512	invalid

Compiler

Compiled 2696 to 1626 computations (39.7% saved)

Details

analyze1.4s (10.1%)

sample80.0ms (0.6%)

simplify7.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite70.0ms (0.5%)

series494.0ms (3.6%)

simplify98.0ms (0.7%)

prune99.0ms (0.7%)

localize13.0ms (0.1%)

rewrite138.0ms (1%)

series1.3s (9.6%)

simplify97.0ms (0.7%)

prune179.0ms (1.3%)

localize12.0ms (0.1%)

rewrite167.0ms (1.2%)

series1.1s (8.4%)

simplify127.0ms (0.9%)

prune158.0ms (1.2%)

localize20.0ms (0.1%)

rewrite209.0ms (1.5%)

series1.3s (9.3%)

simplify115.0ms (0.8%)

prune182.0ms (1.3%)

regimes1.2s (8.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.1s (37.4%)

Profiling