Details

analyze1.1s (8.4%)

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)

sample69.0ms (0.5%)

Algorithm

1×

intervals

Results

30.0ms	106×	body	1024	valid
8.0ms	43×	body	512	valid
6.0ms	9×	body	2048	valid
5.0ms	80×	body	128	valid
2.0ms	18×	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

14.7b

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 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.9b	(cos.f64 (+.f64 a b))

rewrite82.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

24×	`add-sqr-sqrt_binary64_441`
19×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419` `times-frac_binary64_425`
13×	`associate-r_binary64_359`
10×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
5×	`pow1_binary64_480`
3×	`add-log-exp_binary64_458` `associate-/l_binary64_364` `associate-/r_binary64_363` `associate-l_binary64_360`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
1×	`cos-sum_binary64_553` `frac-2neg_binary64_430` `clear-num_binary64_418` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350`

Counts

3 → 67

Calls

3 calls:

8.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

Compiler

Compiled 1186 to 235 computations (80.2% saved)

series505.0ms (3.8%)

Error

13.4b

Counts

3 → 36

Calls

3 calls:

272.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
149.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
46.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1699 to 1043 computations (38.6% saved)

simplify77.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5021	2073

prune106.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Error

0.2b

Counts

104 → 11

Compiler

Compiled 1959 to 576 computations (70.6% saved)

localize12.0ms (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 (sin.f64 b) (sin.f64 a))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))

rewrite157.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-sqr-sqrt_binary64_441`
22×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
20×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`pow1_binary64_480` `associate-/r/_binary64_365`
7×	`sin-mult_binary64_574`
6×	`add-log-exp_binary64_458` `cos-mult_binary64_573` `associate-l_binary64_360`
3×	`frac-sub_binary64_428` `sub-div_binary64_426` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l_binary64_364` `associate-/r_binary64_363` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387`
2×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `pow-prod-down_binary64_490` `*-commutative_binary64_350`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `associate-*r/_binary64_361` `diff-log_binary64_511` `sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 100

Calls

4 calls:

13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
8.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
5.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

Compiler

Compiled 2890 to 436 computations (84.9% saved)

series1.2s (9.1%)

Error

0.2b

Counts

4 → 46

Calls

4 calls:

553.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a)))))
299.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a))))
223.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
94.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

Compiler

Compiled 2545 to 1459 computations (42.7% saved)

simplify88.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4970	3753
1	4970	3753

prune166.0ms (1.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	131	15	146
Fresh	10	0	10
Picked	1	0	1
Done	0	0	0
Total	142	15	157

Error

0.0b

Counts

157 → 15

Compiler

Compiled 3978 to 1025 computations (74.2% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite100.0ms (0.8%)

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:

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

Compiler

Compiled 1946 to 307 computations (84.2% saved)

series936.0ms (7%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

580.0ms	(/.f64 (.f64 (sin.f64 b) r) (-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (*.f64 (sin.f64 b) (sin.f64 a))))
163.0ms	(-.f64 (.f64 (cos.f64 b) (cos.f64 a)) (.f64 (sin.f64 b) (sin.f64 a)))
98.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
64.0ms	(*.f64 (sin.f64 b) r)

Compiler

Compiled 2209 to 1221 computations (44.7% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4952	2404
1	4952	2404

prune111.0ms (0.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	5	9	14
Picked	0	1	1
Done	0	0	0
Total	119	14	133

Error

0.0b

Counts

133 → 14

Compiler

Compiled 2959 to 705 computations (76.2% saved)

localize13.0ms (0.1%)

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

rewrite127.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`add-sqr-sqrt_binary64_441`
22×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
20×	`associate-r_binary64_359`
19×	`times-frac_binary64_425`
13×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
8×	`pow1_binary64_480` `associate-/r/_binary64_365`
7×	`sin-mult_binary64_574`
6×	`add-log-exp_binary64_458` `associate-l_binary64_360` `cos-mult_binary64_573`
3×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `unswap-sqr_binary64_387` `frac-sub_binary64_428` `sub-div_binary64_426` `flip3--_binary64_423` `flip--_binary64_394` `associate-/l_binary64_364` `associate-/r_binary64_363`
2×	`pow-prod-down_binary64_490` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `*-commutative_binary64_350`
1×	`associate-*r/_binary64_361` `frac-2neg_binary64_430` `clear-num_binary64_418` `diff-log_binary64_511` `sub-neg_binary64_412` `cancel-sign-sub-inv_binary64_385`

Counts

4 → 100

Calls

4 calls:

16.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
8.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
5.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Compiler

Compiled 2862 to 437 computations (84.7% saved)

series1.3s (10%)

Error

0.0b

Counts

4 → 49

Calls

4 calls:

573.0ms	(.f64 (sin.f64 b) (/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
473.0ms	(/.f64 r (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
153.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
96.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Compiler

Compiled 2720 to 1531 computations (43.7% saved)

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5035	3889

prune119.0ms (0.9%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	149	14	163

Error

0.0b

Counts

163 → 14

Compiler

Compiled 3582 to 680 computations (81% saved)

regimes1.8s (13.4%)

Accuracy

Total 0.3b remaining (94.6%)

Threshold costs 0.3b (94.6%)

Compiler

Compiled 20343 to 11668 computations (42.6% 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%)

sample5.0s (37.7%)

Algorithm

1×

intervals

Results

1.1s	3528×	body	1024	valid
269.0ms	1372×	body	512	valid
156.0ms	2318×	body	128	valid
121.0ms	190×	body	2048	valid
86.0ms	592×	body	256	valid

Compiler

Compiled 4041 to 2322 computations (42.5% saved)

Details

analyze1.1s (8.4%)

sample69.0ms (0.5%)

simplify7.0ms (0.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite82.0ms (0.6%)

series505.0ms (3.8%)

simplify77.0ms (0.6%)

prune106.0ms (0.8%)

localize12.0ms (0.1%)

rewrite157.0ms (1.2%)

series1.2s (9.1%)

simplify88.0ms (0.7%)

prune166.0ms (1.2%)

localize14.0ms (0.1%)

rewrite100.0ms (0.8%)

series936.0ms (7%)

simplify75.0ms (0.6%)

prune111.0ms (0.8%)

localize13.0ms (0.1%)

rewrite127.0ms (1%)

series1.3s (10%)

simplify71.0ms (0.5%)

prune119.0ms (0.9%)

regimes1.8s (13.4%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.0s (37.7%)

Profiling