Details

analyze45.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 17 to 12 computations (29.4% saved)

sample77.0ms (1.4%)

Algorithm

1×

intervals

Results

30.0ms	57×	body	1024	valid
15.0ms	143×	body	128	valid
9.0ms	34×	body	512	valid
5.0ms	256×	pre	128	true
4.0ms	21×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`associate-/l*_binary64`
2×	`associate-/r/_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	17	17
2	21	17
3	24	17
4	25	17
5	24	17

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.2b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))

Compiler

Compiled 26 to 18 computations (30.8% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
0.1b	(*.f64 e (sin.f64 v))
0.1b	(*.f64 e (cos.f64 v))

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

13×	`add-sqr-sqrt_binary64`
12×	`add-cbrt-cube_binary64`
12×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

3 → 59

Calls

3 calls:

4.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
3.0ms	(*.f64 e (cos.f64 v))
3.0ms	(*.f64 e (sin.f64 v))

Compiler

Compiled 1017 to 368 computations (63.8% saved)

series77.0ms (1.4%)

Error

0.1b

Counts

3 → 30

Calls

3 calls:

32.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
14.0ms	(*.f64 e (cos.f64 v))
13.0ms	(*.f64 e (sin.f64 v))

Compiler

Compiled 1441 to 984 computations (31.7% saved)

simplify102.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-/r*_binary64`
337×	`cancel-sign-sub-inv_binary64`
287×	`associate-/r/_binary64`
259×	`associate-/l/_binary64`
181×	`associate-r_binary64`

Counts

89 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	1717
1	544	1549
2	2088	1515
3	4681	1515
4	4965	1515
5	4966	1515

prune47.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	46	8	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	8	55

Error

0.0b

Counts

55 → 8

Alt Table

Status	Error	Program
	0.8b	(/.f64 1 (/.f64 (+.f64 (.f64 (cos.f64 v) e) 1) (.f64 e (sin.f64 v))))
	0.2b	(.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)) (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)))) (/.f64 (sin.f64 v) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))))
	33.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (.f64 e (cos.f64 v))))
	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
▶	0.2b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2)))) (-.f64 1 (*.f64 e (cos.f64 v))))

Compiler

Compiled 1334 to 721 computations (46% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2))
0.1b	(*.f64 e (sin.f64 v))
0.1b	(*.f64 e (cos.f64 v))
0.3b	(pow.f64 (cos.f64 v) 2)

rewrite113.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`add-exp-log_binary64`
18×	`add-sqr-sqrt_binary64`
14×	`associate-r_binary64`
13×	`add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`

Counts

4 → 84

Calls

4 calls:

6.0ms	(.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2))
3.0ms	(*.f64 e (sin.f64 v))
3.0ms	(*.f64 e (cos.f64 v))
2.0ms	(pow.f64 (cos.f64 v) 2)

Compiler

Compiled 2149 to 951 computations (55.7% saved)

series84.0ms (1.6%)

Error

0.0b

Counts

4 → 33

Calls

4 calls:

19.0ms	(.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2))
19.0ms	(*.f64 e (sin.f64 v))
15.0ms	(*.f64 e (cos.f64 v))
9.0ms	(pow.f64 (cos.f64 v) 2)

Compiler

Compiled 1884 to 1240 computations (34.2% saved)

simplify111.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

480×	`sub-neg_binary64`
377×	`*-commutative_binary64`
373×	`sqr-pow_binary64`
275×	`cancel-sign-sub-inv_binary64`
248×	`associate-l_binary64`

Counts

117 → 77

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	1388
1	401	1163
2	1278	1121
3	2393	1121
4	4172	1094
5	4514	1094
6	5241	1094

prune63.0ms (1.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	77	8	85

Error

0.0b

Counts

85 → 8

Alt Table

Status	Error	Program
	0.8b	(/.f64 1 (/.f64 (+.f64 (.f64 (cos.f64 v) e) 1) (.f64 e (sin.f64 v))))
▶	0.2b	(.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)) (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)))) (/.f64 (sin.f64 v) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))))
	33.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (.f64 e (cos.f64 v))))
	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
✓	0.2b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2)))) (-.f64 1 (*.f64 e (cos.f64 v))))

Compiler

Compiled 1527 to 756 computations (50.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 v) e)
0.1b	(*.f64 (cos.f64 v) e)
0.1b	(*.f64 (cos.f64 v) e)
0.1b	(.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)) (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)))) (/.f64 (sin.f64 v) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))

rewrite194.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

47×	`add-sqr-sqrt_binary64`
33×	`associate-r_binary64`
31×	`add-exp-log_binary64`
28×	`times-frac_binary64`
25×	`*-un-lft-identity_binary64`

Counts

4 → 123

Calls

4 calls:

23.0ms	(.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)) (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)))) (/.f64 (sin.f64 v) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))
3.0ms	(*.f64 (cos.f64 v) e)
3.0ms	(*.f64 (cos.f64 v) e)
3.0ms	(*.f64 (cos.f64 v) e)

Compiler

Compiled 4753 to 2178 computations (54.2% saved)

series108.0ms (2%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

33.0ms	(.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)) (cbrt.f64 (+.f64 (.f64 (cos.f64 v) e) 1)))) (/.f64 (sin.f64 v) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))
17.0ms	(*.f64 (cos.f64 v) e)
16.0ms	(*.f64 (cos.f64 v) e)
16.0ms	(*.f64 (cos.f64 v) e)

Compiler

Compiled 2658 to 1713 computations (35.6% saved)

simplify144.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

507×	`associate-/l/_binary64`
316×	`associate-/r/_binary64`
243×	`cancel-sign-sub-inv_binary64`
222×	`associate-l_binary64`
203×	`associate-r_binary64`

Counts

162 → 138

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	274	5278
1	753	4066
2	2847	4005
3	4975	4005
4	4962	4005

prune139.0ms (2.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	138	8	146

Error

0.0b

Counts

146 → 8

Alt Table

Status	Error	Program
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (.f64 e (cos.f64 v))))
	1.1b	(.f64 (.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 1 (.f64 e (cos.f64 v)))) (cbrt.f64 (+.f64 1 (.f64 e (cos.f64 v)))))) (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (/.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))
	0.8b	(/.f64 1 (/.f64 (+.f64 (.f64 (cos.f64 v) e) 1) (.f64 e (sin.f64 v))))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)))) (cbrt.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1))))
	33.8b	(cbrt.f64 (pow.f64 (/.f64 (.f64 e (sin.f64 v)) (+.f64 (.f64 (cos.f64 v) e) 1)) 3))
	0.5b	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
▶	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
✓	0.2b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2)))) (-.f64 1 (*.f64 e (cos.f64 v))))

Compiler

Compiled 4173 to 2065 computations (50.5% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 (cos.f64 v) e)
0.1b	(/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v))
0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))

rewrite140.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

84×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
55×	`*-un-lft-identity_binary64`
55×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`

Counts

3 → 117

Calls

3 calls:

7.0ms	(/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v))
6.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
3.0ms	(*.f64 (cos.f64 v) e)

Compiler

Compiled 2642 to 1096 computations (58.5% saved)

series91.0ms (1.7%)

Error

0.0b

Counts

3 → 33

Calls

3 calls:

32.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))
24.0ms	(/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v))
13.0ms	(*.f64 (cos.f64 v) e)

Compiler

Compiled 1565 to 1060 computations (32.3% saved)

simplify140.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-/r/_binary64`
405×	`associate-/l/_binary64`
380×	`cancel-sign-sub-inv_binary64`
161×	`associate-r_binary64`
157×	`*-commutative_binary64`

Counts

150 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	313	4200
1	785	3967
2	2684	3921
3	4853	3921
4	4958	3921

prune124.0ms (2.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	128	7	135
Fresh	4	2	6
Picked	0	1	1
Done	0	1	1
Total	132	11	143

Error

0.0b

Counts

143 → 11

Alt Table

Status	Error	Program
	6.3b	(/.f64 e (cbrt.f64 (pow.f64 (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)) 3)))
	1.1b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))) (cbrt.f64 (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))) (/.f64 e (cbrt.f64 (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))))
	1.1b	(/.f64 (.f64 (.f64 (cbrt.f64 e) (cbrt.f64 e)) (.f64 (sin.f64 v) (cbrt.f64 e))) (+.f64 1 (.f64 e (cos.f64 v))))
	1.1b	(.f64 (.f64 (/.f64 e (.f64 (cbrt.f64 (+.f64 1 (.f64 e (cos.f64 v)))) (cbrt.f64 (+.f64 1 (.f64 e (cos.f64 v)))))) (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v)))) (/.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (+.f64 (*.f64 (cos.f64 v) e) 1))))
	0.2b	(.f64 (/.f64 (.f64 e (sin.f64 v)) (-.f64 1 (.f64 (.f64 e e) (pow.f64 (cos.f64 v) 2)))) (-.f64 1 (*.f64 e (cos.f64 v))))
	0.3b	(/.f64 e (/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 v) e) 3) (pow.f64 1 3)) (.f64 (sin.f64 v) (+.f64 1 (.f64 (.f64 e (cos.f64 v)) (-.f64 (*.f64 e (cos.f64 v)) 1))))))
	0.5b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
	33.1b	(/.f64 e (.f64 (sqrt.f64 (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))) (sqrt.f64 (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))))
	1.1b	(.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 v)) (cbrt.f64 (sin.f64 v))) (sqrt.f64 e)) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (cbrt.f64 (sin.f64 v)))))
	33.1b	(/.f64 (/.f64 e (sqrt.f64 (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v)))) (sqrt.f64 (/.f64 (+.f64 (.f64 (cos.f64 v) e) 1) (sin.f64 v))))
	0.3b	(/.f64 e (/.f64 (+.f64 (*.f64 (cos.f64 v) e) 1) (sin.f64 v)))

Compiler

Compiled 2934 to 1334 computations (54.5% saved)

regimes839.0ms (15.7%)

Accuracy

Total 0.1b remaining (87%)

Threshold costs 0.1b (87%)

Compiler

Compiled 18681 to 11543 computations (38.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	35
1	28	35
2	40	35
3	48	35
4	53	35
5	54	35
6	53	35

end1.0ms (0%)

Compiler: Compiled 24 to 16 computations (33.3% saved)

sample2.6s (48.4%)

Algorithm

1×

intervals

Results

1.1s	2010×	body	1024	valid
441.0ms	4500×	body	128	valid
275.0ms	986×	body	512	valid
170.0ms	8000×	pre	128	true
98.0ms	498×	body	256	valid
7.0ms	6×	body	2048	valid

Compiler

Compiled 317 to 199 computations (37.2% saved)

Details

analyze45.0ms (0.8%)

sample77.0ms (1.4%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite53.0ms (1%)

series77.0ms (1.4%)

simplify102.0ms (1.9%)

prune47.0ms (0.9%)

localize16.0ms (0.3%)

rewrite113.0ms (2.1%)

series84.0ms (1.6%)

simplify111.0ms (2.1%)

prune63.0ms (1.2%)

localize13.0ms (0.2%)

rewrite194.0ms (3.6%)

series108.0ms (2%)

simplify144.0ms (2.7%)

prune139.0ms (2.6%)

localize8.0ms (0.2%)

rewrite140.0ms (2.6%)

series91.0ms (1.7%)

simplify140.0ms (2.6%)

prune124.0ms (2.3%)

regimes839.0ms (15.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.6s (48.4%)

Profiling