Details

analyze359.0ms (8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample63.0ms (1.4%)

Algorithm

1×

intervals

Results

26.0ms	53×	body	2048	valid
12.0ms	43×	body	1024	valid
9.0ms	55×	body	512	valid
4.0ms	81×	body	128	valid
2.0ms	21×	body	256	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 20 to 14 computations (30% saved)

simplify31.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

426×	`fma-def_binary64`
293×	`fma-neg_binary64`
85×	`div-sub_binary64`
74×	`associate-/l*_binary64`
63×	`times-frac_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

prune1.0ms (0%)

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

31.5b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	31.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.3b	(-.f64 1 (cos.f64 x))
12.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite135.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

30.5b

Rules

26×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`

Counts

2 → 98

Calls

2 calls:

18.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
14.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 1689 to 738 computations (56.3% saved)

series16.0ms (0.4%)

Error

0.6b

Counts

2 → 8

Calls

2 calls:

6.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
6.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 193 to 142 computations (26.4% saved)

simplify80.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

738×	`associate-/l*_binary64`
439×	`associate-/r*_binary64`
395×	`fma-def_binary64`
245×	`fma-neg_binary64`
225×	`cancel-sign-sub-inv_binary64`

Counts

106 → 49

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	1272
1	353	1162
2	1339	1081
3	4364	1069
4	4914	1069

prune40.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Error

0.0b

Counts

50 → 8

Alt Table

Status	Error	Program
	31.6b	(.f64 (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (.f64 x x))) (sqrt.f64 (/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))))
	56.9b	(/.f64 (-.f64 (/.f64 1 (pow.f64 x 4)) (.f64 (cos.f64 x) (/.f64 (cos.f64 x) (pow.f64 x 4)))) (.f64 (pow.f64 x -2) (+.f64 1 (cos.f64 x))))
	31.4b	(+.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (neg.f64 (.f64 x x))))
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
▶	13.1b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	31.6b	(/.f64 (/.f64 (-.f64 1 (pow.f64 (cos.f64 x) 3)) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (*.f64 x x))
	31.6b	(/.f64 (-.f64 (/.f64 1 (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1)) (/.f64 (pow.f64 (cos.f64 x) 3) (fma.f64 (cos.f64 x) (+.f64 1 (cos.f64 x)) 1))) (*.f64 x x))
	31.9b	(fma.f64 (*.f64 x x) -1/24 1/2)

Compiler

Compiled 838 to 473 computations (43.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.4b	(+.f64 1 (cos.f64 x))
12.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite220.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-cube-cbrt_binary64`
28×	`add-exp-log_binary64`
28×	`pow1_binary64`
22×	`add-cbrt-cube_binary64`
20×	`div-sub_binary64`

Counts

4 → 199

Calls

4 calls:

20.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
16.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
16.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 3887 to 1697 computations (56.3% saved)

series36.0ms (0.8%)

Error

0.0b

Counts

4 → 16

Calls

4 calls:

11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
6.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 542 to 368 computations (32.1% saved)

simplify133.0ms (3%)

Algorithm

1×	egg-herbie

Rules

462×	`fma-def_binary64`
279×	`fma-neg_binary64`
228×	`distribute-rgt-in_binary64`
207×	`distribute-lft-in_binary64`
197×	`cancel-sign-sub-inv_binary64`

Counts

215 → 132

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	3302
1	626	2967
2	2291	2682
3	4792	2682
4	4956	2682

prune93.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	127	5	132
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	133	7	140

Error

Counts

140 → 7

Alt Table

Status	Error	Program
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
▶	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	13.2b	(.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (.f64 x x)))
	13.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))) (*.f64 x x))
✓	13.1b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
	12.9b	(/.f64 1 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))))
	26.1b	(/.f64 (/.f64 (cbrt.f64 (pow.f64 (sin.f64 x) 6)) (+.f64 1 (cos.f64 x))) (*.f64 x x))

Compiler

Compiled 2206 to 1090 computations (50.6% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite146.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-cube-cbrt_binary64`
24×	`add-exp-log_binary64`
19×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 137

Calls

3 calls:

15.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
15.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
13.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 2061 to 1013 computations (50.8% saved)

series37.0ms (0.8%)

Error

Counts

3 → 12

Calls

3 calls:

14.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
10.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
6.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 379 to 280 computations (26.1% saved)

simplify76.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

830×	`associate-/r*_binary64`
729×	`associate-*l/_binary64`
456×	`associate-/l/_binary64`
257×	`associate-/r/_binary64`
121×	`times-frac_binary64`

Counts

149 → 45

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	1946
1	335	1740
2	1370	1724
3	5687	1724

prune29.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	46	6	52

Error

Counts

52 → 6

Alt Table

Status	Error	Program
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
✓	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	13.2b	(.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (.f64 x x)))
	13.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))) (*.f64 x x))
▶	12.9b	(/.f64 1 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))))
	12.9b	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (.f64 x (.f64 x (cos.f64 (*.f64 1/2 x)))))

Compiler

Compiled 612 to 349 computations (43% saved)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.2b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
0.4b	(/.f64 1 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))))
12.2b	(/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))))

rewrite144.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-exp-log_binary64`
26×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
19×	`add-cbrt-cube_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 140

Calls

3 calls:

18.0ms	(/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))))
16.0ms	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
14.0ms	(/.f64 1 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))))

Compiler

Compiled 2370 to 1403 computations (40.8% saved)

series41.0ms (0.9%)

Error

Counts

3 → 12

Calls

3 calls:

14.0ms	(/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))))
10.0ms	(/.f64 1 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))))
10.0ms	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

Compiler

Compiled 429 to 333 computations (22.4% saved)

simplify120.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

487×	`associate-*l/_binary64`
459×	`fma-def_binary64`
390×	`associate-*r/_binary64`
382×	`associate-/l/_binary64`
278×	`*-commutative_binary64`

Counts

152 → 69

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2476
1	342	2116
2	1221	2107
3	4224	2107
4	4984	2107
5	4967	2107

prune45.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	69	6	75

Error

Counts

75 → 6

Alt Table

Status	Error	Program
	31.3b	(*.f64 (-.f64 1 (cos.f64 x)) (pow.f64 x -2))
	0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
	13.2b	(.f64 (tan.f64 (/.f64 x 2)) (/.f64 (sin.f64 x) (.f64 x x)))
	13.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (.f64 (cbrt.f64 (pow.f64 (+.f64 1 (cos.f64 x)) 2)) (cbrt.f64 (+.f64 1 (cos.f64 x))))) (*.f64 x x))
	12.9b	(/.f64 1 (/.f64 (.f64 x x) (.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))))
	12.9b	(/.f64 (.f64 (sin.f64 (.f64 1/2 x)) (sin.f64 x)) (.f64 x (.f64 x (cos.f64 (*.f64 1/2 x)))))

Compiler

Compiled 947 to 560 computations (40.9% saved)

regimes399.0ms (8.9%)

Accuracy

Total 0.1b remaining (90.4%)

Threshold costs 0.1b (90.4%)

Compiler

Compiled 7098 to 4793 computations (32.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	9	17

end1.0ms (0%)

Compiler: Compiled 12 to 8 computations (33.3% saved)

sample2.2s (49.2%)

Algorithm

1×

intervals

Results

1.1s	2012×	body	2048	valid
289.0ms	1103×	body	1024	valid
250.0ms	1497×	body	512	valid
140.0ms	2528×	body	128	valid
89.0ms	755×	body	256	valid
47.0ms	105×	body	4096	valid

Compiler

Compiled 111 to 77 computations (30.6% saved)

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12

Details

analyze359.0ms (8%)

sample63.0ms (1.4%)

simplify31.0ms (0.7%)

prune1.0ms (0%)

localize6.0ms (0.1%)

rewrite135.0ms (3%)

series16.0ms (0.4%)

simplify80.0ms (1.8%)

prune40.0ms (0.9%)

localize10.0ms (0.2%)

rewrite220.0ms (4.9%)

series36.0ms (0.8%)

simplify133.0ms (3%)

prune93.0ms (2.1%)

localize11.0ms (0.2%)

rewrite146.0ms (3.2%)

series37.0ms (0.8%)

simplify76.0ms (1.7%)

prune29.0ms (0.6%)

localize13.0ms (0.3%)

rewrite144.0ms (3.2%)

series41.0ms (0.9%)

simplify120.0ms (2.7%)

prune45.0ms (1%)

regimes399.0ms (8.9%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample2.2s (49.2%)

Profiling

Iter	Nodes	Cost
0	7	12
1	16	12
2	27	12
3	40	12
4	72	12
5	110	12
6	158	12
7	253	12
8	383	12
9	526	12
10	640	12
11	625	12
12	570	12