Details

analyze1.8s (11.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample9.2s (58.9%)

Results

5.1s	2132×	body	2048	valid
2.3s	3100×	body	1024	valid
893.0ms	1575×	body	512	valid
384.0ms	598×	body	128	valid
202.0ms	742×	body	256	valid
154.0ms	109×	body	4096	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify85.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

583×	`fma-neg_binary64`
430×	`div-sub_binary64`
430×	`fma-def_binary64`
335×	`times-frac_binary64`
160×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	14
1	14	14
2	24	14
3	41	14
4	67	14
5	115	14
6	212	14
7	416	14
8	699	14
9	1176	14
10	1555	14
11	1621	14
12	1652	14
13	1679	14
14	1689	14
15	1693	14
16	1693	14
17	1592	14

prune2.0ms (0%)

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

31.3b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.3b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	0.8b	(-.f64 x (tan.f64 x))
✓	0.8b	(-.f64 x (sin.f64 x))

series18.0ms (0.1%)

Counts

3 → 30

Calls

3 calls:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))
2.0ms	(-.f64 x (sin.f64 x))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`*-un-lft-identity_binary64`
59×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
18×	`prod-diff_binary64`

Counts

3 → 114

Calls

3 calls:

8.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
3.0ms	(-.f64 x (tan.f64 x))
3.0ms	(-.f64 x (sin.f64 x))

simplify107.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

815×	`fma-def_binary64`
368×	`fma-neg_binary64`
252×	`associate-/l/_binary64`
250×	`cancel-sign-sub-inv_binary64`
202×	`distribute-rgt-in_binary64`

Counts

144 → 152

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	3004
1	594	2580
2	1993	2458
3	4734	2458
4	4868	2458

prune78.0ms (0.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	151	2	153

Error

0.0b

Counts

153 → 2

Alt Table

Status	Error	Program
	31.9b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
▶	31.3b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

Compiler

Compiled 3140 to 879 computations (72% saved)

localize8.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 x (tan.f64 x)))
✓	0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
✓	0.6b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
	0.8b	(-.f64 x (tan.f64 x))

series27.0ms (0.2%)

Counts

3 → 36

Calls

3 calls:

12.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
8.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
7.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

rewrite240.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

727×	`*-un-lft-identity_binary64`
717×	`add-sqr-sqrt_binary64`
708×	`times-frac_binary64`
441×	`prod-diff_binary64`
421×	`add-cube-cbrt_binary64`

Counts

3 → 591

Calls

3 calls:

31.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
5.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(/.f64 x (-.f64 x (tan.f64 x)))

simplify1.4s (9.1%)

Algorithm

1×	egg-herbie

Rules

461×	`fma-neg_binary64`
412×	`unsub-neg_binary64`
312×	`fma-udef_binary64`
280×	`sub-neg_binary64`
250×	`associate-+r-_binary64`

Counts

627 → 574

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	622	41023
1	1422	27517
2	3251	20234
3	4263	20192
4	4884	20192
5	4829	20192

prune381.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	657	1	658
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	658	2	660

Error

Counts

660 → 2

Alt Table

Status	Error	Program
▶	31.3b	(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))
	31.9b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Status

Error

Program

▶

31.3b

(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))

31.9b

(-.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 34024 to 4873 computations (85.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))
✓	0.6b	(fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))
	0.8b	(-.f64 x (tan.f64 x))
✓	30.1b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))

series361.0ms (2.3%)

Counts

3 → 36

Calls

3 calls:

334.0ms

(fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))

15.0ms

(*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))

12.0ms

(fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
21×	`associate-l_binary64`
20×	`*-un-lft-identity_binary64`
17×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 65

Calls

3 calls:

8.0ms

(*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))

0.0ms

(fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))

0.0ms

(fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

883×	`times-frac_binary64`
419×	`associate-/l*_binary64`
372×	`associate-l_binary64`
281×	`fma-def_binary64`
256×	`associate-/r*_binary64`

Counts

101 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2080
1	370	1836
2	1149	1708
3	4661	1684
4	4934	1684

prune291.0ms (1.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	387	0	387
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	387	2	389

Error

Counts

389 → 2

Alt Table

Status	Error	Program
✓	31.3b	(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))
▶	31.9b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Status

Error

Program

✓

31.3b

(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))

▶

31.9b

(-.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 18285 to 6899 computations (62.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
✓	0.0b	(*.f64 27/112000 (pow.f64 x 6))
✓	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	19.7b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series14.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

4.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
4.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
3.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
9×	`add-exp-log_binary64`
9×	`prod-diff_binary64`

Counts

4 → 79

Calls

4 calls:

4.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))
0.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)
0.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))

simplify122.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

445×	`fma-neg_binary64`
370×	`fma-def_binary64`
341×	`distribute-rgt-in_binary64`
340×	`distribute-lft-in_binary64`
292×	`exp-prod_binary64`

Counts

115 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	2086
1	260	1929
2	799	1728
3	2810	1715
4	4377	1706
5	4997	1706
6	4754	1706

prune117.0ms (0.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	125	2	127

Error

Counts

127 → 2

Alt Table

Status	Error	Program
✓	31.3b	(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))
✓	31.9b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Status

Error

Program

✓

31.3b

(+.f64 (fma.f64 1 (/.f64 x (-.f64 x (tan.f64 x))) (neg.f64 (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x)))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 x (tan.f64 x)))) (sin.f64 x) (*.f64 (/.f64 1 (-.f64 x (tan.f64 x))) (sin.f64 x))))

✓

31.9b

(-.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/112000 (pow.f64 x 6))) (fma.f64 27/2800 (pow.f64 x 4) 1/2))

Compiler

Compiled 3428 to 2562 computations (25.3% saved)

regimes1.0s (6.5%)

Accuracy

Total 0.0b remaining (71.6%)

Threshold costs 0.0b (71.6%)

Counts

293 → 3

Compiler

Compiled 14329 to 7181 computations (49.9% saved)

bsearch61.0ms (0.4%)

Steps

Iters	Range		Point
10	1.5772227619424086e-7	980.049692893398	0.005566771948535619
8	-0.0592193551147717	-2.7210276697383724e-6	-0.004881470445787531

Compiler

Compiled 2 to 1 computations (50% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`+-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	34	118
1	54	118
2	66	118
3	72	118
4	74	118
5	71	118

end89.0ms (0.6%)

Compiler: Compiled 213 to 115 computations (46% saved)

Details

analyze1.8s (11.5%)

sample9.2s (58.9%)

simplify85.0ms (0.5%)

prune2.0ms (0%)

localize7.0ms (0%)

series18.0ms (0.1%)

rewrite21.0ms (0.1%)

simplify107.0ms (0.7%)

prune78.0ms (0.5%)

localize8.0ms (0%)

series27.0ms (0.2%)

rewrite240.0ms (1.5%)

simplify1.4s (9.1%)

prune381.0ms (2.4%)

localize15.0ms (0.1%)

series361.0ms (2.3%)

rewrite13.0ms (0.1%)

simplify90.0ms (0.6%)

prune291.0ms (1.9%)

localize11.0ms (0.1%)

series14.0ms (0.1%)

rewrite11.0ms (0.1%)

simplify122.0ms (0.8%)

prune117.0ms (0.8%)

regimes1.0s (6.5%)

bsearch61.0ms (0.4%)

simplify4.0ms (0%)

end89.0ms (0.6%)

Profiling