Details

analyze1.1s (13.5%)

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)

sample81.0ms (1%)

Algorithm

1×

intervals

Results

42.0ms	87×	body	1280	valid
18.0ms	61×	body	640	valid
5.0ms	74×	body	80	valid
5.0ms	24×	body	320	valid
1.0ms	10×	body	160	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify25.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

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

Merged error: 12.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize10.0ms (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)))
1.8b	(cos.f64 (+.f64 a b))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64` `insert-posit16`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `cos-sum_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

3 → 50

Calls

3 calls:

7.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))
5.0ms	(*.f64 r (sin.f64 b))

series304.0ms (3.8%)

Counts

3 → 9

Calls

3 calls:

214.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
63.0ms	(*.f64 r (sin.f64 b))
28.0ms	(cos.f64 (+.f64 a b))

simplify149.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4871	724
1	4871	724

prune55.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	50	9	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	9	60

Merged error: 0.1b

Counts

60 → 9

Compiler

Compiled 876 to 253 computations (71.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`sin-mult_binary64`
4×	`cos-mult_binary64` `associate-/r/_binary64` `insert-posit16`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 79

Calls

4 calls:

12.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
7.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
6.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
5.0ms	(*.f64 r (sin.f64 b))

series730.0ms (9%)

Counts

4 → 12

Calls

4 calls:

457.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
145.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
71.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
56.0ms	(*.f64 r (sin.f64 b))

simplify127.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	6289	1614

prune101.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	90	10	100

Merged error: 0.0b

Counts

100 → 10

Compiler

Compiled 2177 to 452 computations (79.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite45.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`associate-r_binary64`
19×	`times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-/r/_binary64`
7×	`sin-mult_binary64`
6×	`add-log-exp_binary64` `cos-mult_binary64` `associate-l_binary64`
4×	`insert-posit16`
3×	`associate-/r_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 103

Calls

4 calls:

17.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
11.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
7.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
6.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

series946.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

462.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
256.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
147.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
81.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify141.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	6019	2922

prune113.0ms (1.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	115	10	125

Merged error: 0.0b

Counts

125 → 10

Compiler

Compiled 3088 to 599 computations (80.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
1.7b	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64`
4×	`insert-posit16`
3×	`associate-/r_binary64` `associate--r+_binary64` `associate-r_binary64` `log-pow_binary64` `associate-l*_binary64` `times-frac_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `associate-/l_binary64` `div-inv_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
11.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
6.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
3.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

series758.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

463.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
145.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (.f64 (sin.f64 b) (sin.f64 a)))))
75.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
74.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

simplify126.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4970	1643
1	4970	1643

prune76.0ms (0.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

Compiler

Compiled 1920 to 340 computations (82.3% saved)

regimes81.0ms (1%)

Compiler: Compiled 912 to 465 computations (49% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample3.0s (37%)

Algorithm

1×

intervals

Results

1.4s	2934×	body	1280	valid
535.0ms	1806×	body	640	valid
211.0ms	357×	body	160	valid
164.0ms	2163×	body	80	valid
153.0ms	740×	body	320	valid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Compiler

Compiled 328 to 173 computations (47.3% saved)

Details

analyze1.1s (13.5%)

sample81.0ms (1%)

simplify25.0ms (0.3%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite18.0ms (0.2%)

series304.0ms (3.8%)

simplify149.0ms (1.8%)

prune55.0ms (0.7%)

localize15.0ms (0.2%)

rewrite32.0ms (0.4%)

series730.0ms (9%)

simplify127.0ms (1.6%)

prune101.0ms (1.2%)

localize15.0ms (0.2%)

rewrite45.0ms (0.6%)

series946.0ms (11.7%)

simplify141.0ms (1.7%)

prune113.0ms (1.4%)

localize17.0ms (0.2%)

rewrite34.0ms (0.4%)

series758.0ms (9.4%)

simplify126.0ms (1.6%)

prune76.0ms (0.9%)

regimes81.0ms (1%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.0s (37%)

Profiling