Details

analyze1.2s (19.7%)

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
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample73.0ms (1.2%)

Algorithm

1×

intervals

Results

38.0ms	82×	body	1024	valid
12.0ms	113×	body	128	valid
10.0ms	42×	body	512	valid
3.0ms	19×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 31 to 25 computations (19.4% saved)

simplify15.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

27×	`cancel-sign-sub-inv_binary64`
22×	`sub-neg_binary64`
11×	`associate-/l*_binary64`
11×	`distribute-rgt-in_binary64`
10×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
	0.2b	(+.f64 (neg.f64 (*.f64 x (/.f64 1 (tan.f64 B)))) (/.f64 1 (sin.f64 B)))

Compiler

Compiled 61 to 46 computations (24.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))

rewrite98.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
14×	`cancel-sign-sub-inv_binary64`

Counts

3 → 94

Calls

3 calls:

13.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
3.0ms	(/.f64 x (tan.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1508 to 610 computations (59.5% saved)

series130.0ms (2.1%)

Error

0.1b

Counts

3 → 26

Calls

3 calls:

73.0ms	(/.f64 x (tan.f64 B))
39.0ms	(-.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B)))
7.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 862 to 565 computations (34.5% saved)

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

378×	`associate-+l+_binary64`
338×	`associate-/l*_binary64`
257×	`associate-r_binary64`
254×	`associate-+r+_binary64`
244×	`associate-l_binary64`

Counts

120 → 64

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	196	1862
1	491	1809
2	1347	1806
3	4372	1806
4	4977	1806

prune34.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	57	7	64
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	59	7	66

Error

0.0b

Counts

66 → 7

Alt Table

Status	Error	Program
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
	23.0b	(/.f64 (-.f64 (/.f64 (/.f64 1 (sin.f64 B)) (sin.f64 B)) (*.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))))
	31.1b	(/.f64 (-.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3) (pow.f64 (/.f64 x (tan.f64 B)) 3)) (+.f64 (*.f64 (/.f64 x (tan.f64 B)) (/.f64 x (tan.f64 B))) (/.f64 (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 x (tan.f64 B))) (sin.f64 B))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	17.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	31.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))

Compiler

Compiled 880 to 451 computations (48.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
0.1b	(/.f64 1 (sin.f64 B))
0.1b	(*.f64 x (cos.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))

rewrite99.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`
13×	`times-frac_binary64`

Counts

4 → 93

Calls

4 calls:

12.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
6.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms	(*.f64 x (cos.f64 B))
2.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1661 to 599 computations (63.9% saved)

series154.0ms (2.5%)

Error

0.0b

Counts

4 → 34

Calls

4 calls:

94.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
23.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
15.0ms	(*.f64 x (cos.f64 B))
8.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 1244 to 806 computations (35.2% saved)

simplify193.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

442×	`associate-+l+_binary64`
276×	`associate-/r*_binary64`
269×	`associate-/l/_binary64`
253×	`associate-/r/_binary64`
220×	`cancel-sign-sub-inv_binary64`

Counts

127 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2117
1	499	1951
2	1775	1934
3	4698	1934
4	4987	1934

prune42.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Error

0.0b

Counts

89 → 7

Alt Table

Status	Error	Program
▶	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	23.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	17.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	31.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))

Compiler

Compiled 1064 to 496 computations (53.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
0.1b	(/.f64 1 (sin.f64 B))
0.2b	(/.f64 (cos.f64 B) (sin.f64 B))
0.3b	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))

rewrite174.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
28×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 107

Calls

4 calls:

8.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
6.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
3.0ms	(/.f64 (cos.f64 B) (sin.f64 B))
3.0ms	(/.f64 1 (sin.f64 B))

Compiler

Compiled 2095 to 727 computations (65.3% saved)

series87.0ms (1.4%)

Error

0.0b

Counts

4 → 31

Calls

4 calls:

34.0ms	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
23.0ms	(*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))
9.0ms	(/.f64 1 (sin.f64 B))
8.0ms	(/.f64 (cos.f64 B) (sin.f64 B))

Compiler

Compiled 1133 to 743 computations (34.4% saved)

simplify150.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

497×	`times-frac_binary64`
349×	`associate-/l*_binary64`
259×	`cancel-sign-sub-inv_binary64`
231×	`div-sub_binary64`
214×	`neg-mul-1_binary64`

Counts

138 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2394
1	516	2219
2	1834	2210
3	4116	2210
4	5008	2210

prune40.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	84	7	91

Error

0.0b

Counts

91 → 7

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
▶	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	23.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	17.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	31.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))

Compiler

Compiled 1176 to 514 computations (56.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite66.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

Compiler

Compiled 1421 to 438 computations (69.2% saved)

series66.0ms (1.1%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)
14.0ms	(cbrt.f64 x)

Compiler

Compiled 646 to 443 computations (31.4% saved)

simplify228.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

599×	`associate-/l*_binary64`
494×	`log-prod_binary64`
484×	`unswap-sqr_binary64`
309×	`distribute-rgt-neg-in_binary64`
281×	`distribute-lft-neg-in_binary64`

Counts

85 → 64

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	81	803
1	165	723
2	600	709
3	1315	695
4	4524	571
5	4354	571
6	4308	571
7	4919	571
8	4947	571

prune30.0ms (0.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	64	7	71

Error

0.0b

Counts

71 → 7

Alt Table

Status	Error	Program
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (*.f64 x (/.f64 (cos.f64 B) (sin.f64 B)))))
✓	0.6b	(-.f64 (/.f64 1 (sin.f64 B)) (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (/.f64 (cbrt.f64 x) (tan.f64 B))))
	23.1b	(/.f64 (-.f64 (/.f64 1 (.f64 (sin.f64 B) (sin.f64 B))) (.f64 (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)) (/.f64 (.f64 x (cos.f64 B)) (sin.f64 B)))) (+.f64 (/.f64 1 (sin.f64 B)) (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
✓	0.2b	(+.f64 (/.f64 1 (sin.f64 B)) (neg.f64 (/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))))
	11.5b	(/.f64 (-.f64 (tan.f64 B) (.f64 (sin.f64 B) x)) (.f64 (sin.f64 B) (tan.f64 B)))
	17.3b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 1 (sin.f64 B)) 3)) (/.f64 x (tan.f64 B)))
	31.3b	(-.f64 (/.f64 1 (sin.f64 B)) (*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (tan.f64 B))))

Compiler

Compiled 653 to 304 computations (53.4% saved)

regimes643.0ms (10.4%)

Accuracy

Total 0.1b remaining (82.2%)

Threshold costs 0.1b (82.2%)

Compiler

Compiled 8083 to 5364 computations (33.6% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	18	14
2	23	14
3	26	14
4	27	14
5	26	14

end2.0ms (0%)

Compiler: Compiled 11 to 8 computations (27.3% saved)

sample2.5s (40.4%)

Algorithm

1×

intervals

Results

1.2s	2242×	body	1024	valid
390.0ms	4007×	body	128	valid
324.0ms	1190×	body	512	valid
140.0ms	552×	body	256	valid
14.0ms	156×	body	128	invalid
8.0ms	9×	body	2048	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 158 to 97 computations (38.6% saved)

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14

Details

analyze1.2s (19.7%)

sample73.0ms (1.2%)

simplify15.0ms (0.3%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

rewrite98.0ms (1.6%)

series130.0ms (2.1%)

simplify91.0ms (1.5%)

prune34.0ms (0.5%)

localize9.0ms (0.1%)

rewrite99.0ms (1.6%)

series154.0ms (2.5%)

simplify193.0ms (3.1%)

prune42.0ms (0.7%)

localize11.0ms (0.2%)

rewrite174.0ms (2.8%)

series87.0ms (1.4%)

simplify150.0ms (2.4%)

prune40.0ms (0.6%)

localize13.0ms (0.2%)

rewrite66.0ms (1.1%)

series66.0ms (1.1%)

simplify228.0ms (3.7%)

prune30.0ms (0.5%)

regimes643.0ms (10.4%)

simplify4.0ms (0.1%)

end2.0ms (0%)

sample2.5s (40.4%)

Profiling

Iter	Nodes	Cost
0	11	19
1	24	14
2	45	14
3	73	14
4	102	14
5	129	14
6	136	14
7	171	14
8	162	14
9	168	14
10	165	14
11	140	14