Details

analyze1.8s (13.6%)

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)

sample9.1s (69.6%)

Results

5.6s	2026×	body	2048	valid
2.1s	3148×	body	1024	valid
745.0ms	1554×	body	512	valid
196.0ms	754×	body	256	valid
180.0ms	660×	body	128	valid
153.0ms	114×	body	4096	valid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify82.0ms (0.6%)

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

32.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	32.8b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
✓	1.9b	(-.f64 x (tan.f64 x))
✓	1.9b	(-.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))
3.0ms	(-.f64 x (sin.f64 x))

rewrite150.0ms (1.1%)

Algorithm

2×	batch-egg-rewrite

Rules

336× egg-rr

Counts

3 → 336

Calls

2 calls:

133.0ms	((-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)) (/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	26
1	170	26
2	2622	26
3	5193	26
0	0	0
1	0	0

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

419×	`unswap-sqr_binary64`
338×	`times-frac_binary64`
303×	`fma-def_binary64`
278×	`sub-neg_binary64`
224×	`distribute-rgt-neg-in_binary64`

Counts

366 → 367

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	658
1	258	654
2	840	614
3	3583	602
4	4943	602

prune277.0ms (2.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	365	2	367
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	366	2	368

Error

0.0b

Counts

368 → 2

Alt Table

Status	Error	Program
	33.0b	(+.f64 1 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (-.f64 (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
▶	30.5b	(-.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

33.0b

(+.f64 1 (+.f64 (/.f64 (sin.f64 x) (*.f64 x (cos.f64 x))) (-.f64 (*.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))))

▶

30.5b

(-.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 16685 to 4069 computations (75.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.1%)

Counts

4 → 36

Calls

4 calls:

7.0ms	(-.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))
4.0ms	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
3.0ms	(*.f64 27/112000 (pow.f64 x 6))
3.0ms	(fma.f64 27/2800 (pow.f64 x 4) 1/2)

rewrite72.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

110× egg-rr

Counts

4 → 110

Calls

2 calls:

70.0ms

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

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	53
1	325	53
2	3290	53
3	4889	53
0	0	0
1	0	0

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

829×	`distribute-rgt-neg-in_binary64`
802×	`fma-neg_binary64`
670×	`distribute-lft-neg-in_binary64`
618×	`cancel-sign-sub-inv_binary64`
344×	`neg-mul-1_binary64`

Counts

146 → 129

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	424
1	62	416
2	133	408
3	374	408
4	1238	408
5	3147	408
6	4625	408
7	5121	408

prune111.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	128	3	131

Error

0.0b

Counts

131 → 3

Alt Table

Status	Error	Program
	30.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
	33.0b	(+.f64 1 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (-.f64 (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))))
▶	30.5b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))) 1))

Compiler

Compiled 3464 to 2602 computations (24.9% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6)))
✓	0.5b	(exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2)))
✓	19.7b	(-.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))) 1))
✓	24.0b	(log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))

series33.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

20.0ms

(exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2)))

7.0ms

(log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))

6.0ms

(-.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/112000 (pow.f64 x 6))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))) 1))

rewrite72.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

100× egg-rr

Counts

3 → 100

Calls

2 calls:

70.0ms

((log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2)) (-.f64 (fma.f64 9/40 (*.f64 x x) (*.f64 27/112000 (pow.f64 x 6))) (-.f64 (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))) 1)) (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	46
1	388	45
2	4020	45
3	4887	45
0	0	0
1	0	0

simplify95.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

577×	`cancel-sign-sub-inv_binary64`
484×	`sub-neg_binary64`
480×	`times-frac_binary64`
381×	`fma-neg_binary64`
232×	`fma-def_binary64`

Counts

136 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	83	577
1	244	553
2	681	533
3	2093	501
4	4296	501
5	3975	501
6	4908	501
7	4720	501

prune159.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	172	1	173
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	173	3	176

Error

Counts

176 → 3

Alt Table

Status	Error	Program
	30.5b	(-.f64 (-.f64 (exp.f64 (log1p.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))))) 1) (-.f64 (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))) 1))
▶	30.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
	33.0b	(+.f64 1 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (-.f64 (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))))

Compiler

Compiled 5030 to 3907 computations (22.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 27/112000 (pow.f64 x 6) -1/2)
✓	0.1b	(fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800))
✓	0.2b	(*.f64 (pow.f64 x 3) -27/2800)
✓	16.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))

series15.0ms (0.1%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
3.0ms	(fma.f64 27/112000 (pow.f64 x 6) -1/2)
3.0ms	(fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800))
3.0ms	(*.f64 (pow.f64 x 3) -27/2800)

rewrite67.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

101× egg-rr

Counts

4 → 101

Calls

2 calls:

62.0ms

((fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2)) (*.f64 (pow.f64 x 3) -27/2800) (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))

0.0ms

()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	294	48
2	2924	48
3	4911	48
0	0	0
1	0	0

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

468×	`unswap-sqr_binary64`
438×	`associate-l_binary64`
419×	`distribute-rgt-neg-in_binary64`
382×	`distribute-lft-neg-in_binary64`
326×	`associate-r_binary64`

Counts

149 → 119

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	496
1	82	470
2	190	462
3	538	462
4	1829	462
5	4935	462
6	4950	462
7	4935	462

prune107.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	119	3	122

Error

Counts

122 → 3

Alt Table

Status	Error	Program
	30.5b	(-.f64 (-.f64 (exp.f64 (log1p.f64 (fma.f64 9/40 (.f64 x x) (.f64 27/112000 (pow.f64 x 6))))) 1) (-.f64 (exp.f64 (log1p.f64 (fma.f64 27/2800 (pow.f64 x 4) 1/2))) 1))
✓	30.5b	(fma.f64 x (fma.f64 9/40 x (*.f64 (pow.f64 x 3) -27/2800)) (fma.f64 27/112000 (pow.f64 x 6) -1/2))
	33.0b	(+.f64 1 (+.f64 (/.f64 (sin.f64 x) (.f64 x (cos.f64 x))) (-.f64 (.f64 (/.f64 (sin.f64 x) (*.f64 x x)) (-.f64 (/.f64 (sin.f64 x) (pow.f64 (cos.f64 x) 2)) (/.f64 (sin.f64 x) (cos.f64 x)))) (/.f64 (sin.f64 x) x))))

Compiler

Compiled 2603 to 2044 computations (21.5% saved)

regimes454.0ms (3.5%)

Accuracy

Total -0.1b remaining (-101.7%)

Threshold costs -0.1b (-101.7%)

Counts

157 → 3

Compiler

Compiled 6234 to 3808 computations (38.9% saved)

bsearch58.0ms (0.4%)

Steps

Iters	Range		Point
9	0.051859422883366	31356.31780747472	2.788871323292318
9	-2283252.67822101	-0.023847521134197004	-0.09522604487482855

Compiler

Compiled 2 to 1 computations (50% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`*-commutative_binary64`
8×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	129
1	67	129
2	82	129
3	90	129
4	93	129
5	92	129

end116.0ms (0.9%)

Compiler: Compiled 247 to 149 computations (39.7% saved)

Details

analyze1.8s (13.6%)

sample9.1s (69.6%)

simplify82.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series18.0ms (0.1%)

rewrite150.0ms (1.1%)

simplify99.0ms (0.8%)

prune277.0ms (2.1%)

localize10.0ms (0.1%)

series17.0ms (0.1%)

rewrite72.0ms (0.6%)

simplify75.0ms (0.6%)

prune111.0ms (0.8%)

localize15.0ms (0.1%)

series33.0ms (0.3%)

rewrite72.0ms (0.5%)

simplify95.0ms (0.7%)

prune159.0ms (1.2%)

localize9.0ms (0.1%)

series15.0ms (0.1%)

rewrite67.0ms (0.5%)

simplify84.0ms (0.6%)

prune107.0ms (0.8%)

regimes454.0ms (3.5%)

bsearch58.0ms (0.4%)

simplify5.0ms (0%)

end116.0ms (0.9%)

Profiling