Details

analyze1.0s (12.4%)

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)

sample75.0ms (0.9%)

Algorithm

1×

intervals

Results

43.0ms	114×	body	1024	valid
7.0ms	32×	body	512	valid
7.0ms	8×	body	2048	valid
5.0ms	78×	body	128	valid
4.0ms	24×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify8.0ms (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

Merged error: 13.5b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.4b	(cos.f64 (+.f64 a b))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

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

series349.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

222.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
100.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
27.0ms	(cos.f64 (+.f64 a b))

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5764	1258

prune255.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 0.1b

Counts

77 → 11

Compiler

Compiled 4302 to 2307 computations (46.4% 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 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)))))
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))))

rewrite47.0ms (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`
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` `cancel-sign-sub-inv_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 100

Calls

4 calls:

17.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

series969.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

483.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
273.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
144.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
68.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify80.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5450	2752

prune652.0ms (8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	9	1	10
Picked	0	1	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

Compiler

Compiled 13804 to 6489 computations (53% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
0.3b	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
29.7b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `times-frac_binary64`
8×	`cbrt-prod_binary64`
4×	`add-log-exp_binary64` `sin-mult_binary64`
3×	`pow-unpow_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-/r/_binary64` `associate-l_binary64` `cube-div_binary64` `associate-/l_binary64`
2×	`cbrt-div_binary64` `pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `cos-mult_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (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))

series540.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 b) (sin.f64 a)) 3))))
144.0ms	(pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3)
68.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 b) (sin.f64 a)) 3))
65.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5137	1881

prune135.0ms (1.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	102	14	116

Merged error: 0.0b

Counts

116 → 14

Compiler

Compiled 3348 to 1134 computations (66.1% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(*.f64 (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)))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/r*_binary64` `pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
3×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `flip3--_binary64` `cos-mult_binary64` `flip--_binary64`

Counts

4 → 97

Calls

4 calls:

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

series731.0ms (9%)

Counts

4 → 12

Calls

4 calls:

455.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
136.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
74.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
67.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5089	2117

prune191.0ms (2.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	11	11
Picked	1	0	1
Done	0	2	2
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

Compiler

Compiled 6302 to 1246 computations (80.2% saved)

regimes107.0ms (1.3%)

Compiler: Compiled 1368 to 690 computations (49.6% 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%)

sample2.6s (31.9%)

Algorithm

1×

intervals

Results

1.3s	3587×	body	1024	valid
300.0ms	1331×	body	512	valid
167.0ms	2310×	body	128	valid
165.0ms	188×	body	2048	valid
91.0ms	584×	body	256	valid
0.0ms	1×	body	1024	invalid

Compiler

Compiled 480 to 248 computations (48.3% saved)

Details

analyze1.0s (12.4%)

sample75.0ms (0.9%)

simplify8.0ms (0.1%)

prune2.0ms (0%)

localize14.0ms (0.2%)

rewrite23.0ms (0.3%)

series349.0ms (4.3%)

simplify89.0ms (1.1%)

prune255.0ms (3.1%)

localize15.0ms (0.2%)

rewrite47.0ms (0.6%)

series969.0ms (11.9%)

simplify80.0ms (1%)

prune652.0ms (8%)

localize17.0ms (0.2%)

rewrite37.0ms (0.5%)

series540.0ms (6.6%)

simplify56.0ms (0.7%)

prune135.0ms (1.7%)

localize21.0ms (0.3%)

rewrite42.0ms (0.5%)

series731.0ms (9%)

simplify72.0ms (0.9%)

prune191.0ms (2.3%)

regimes107.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (31.9%)

Profiling