Details

analyze3.6s (26.5%)

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
0%	99.9%	0.1%	6
9.4%	90.5%	0.1%	7
14%	85.8%	0.1%	8
16.4%	83.5%	0.1%	9
24.6%	75.3%	0.1%	10
28.7%	71.2%	0.1%	11
30.7%	69.1%	0.1%	12
35.8%	64%	0.1%	13
38.4%	61.5%	0.1%	14

Compiler

Compiled 32 to 18 computations (43.8% saved)

sample5.9s (43.5%)

Results

3.2s	2076×	body	1024	valid
1.5s	4684×	body	128	valid
860.0ms	973×	body	512	valid
310.0ms	517×	body	256	valid
21.0ms	6×	body	2048	valid

Compiler

Compiled 95 to 53 computations (44.2% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Rules

12×	`fma-def_binary64`
11×	`*-commutative_binary64`
6×	`associate-r_binary64`
6×	`associate-l_binary64`
1×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	44
1	30	44
2	50	44
3	56	44
4	56	44

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 118 to 51 computations (56.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 eh (cos.f64 t))
✓	0.1b	(*.f64 ew (sin.f64 t))
✓	3.7b	(/.f64 (/.f64 eh ew) (tan.f64 t))
✓	35.2b	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

series98.0ms (0.7%)

Counts

4 → 120

Calls

4 calls:

67.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))
18.0ms	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))
6.0ms	(*.f64 ew (sin.f64 t))
6.0ms	(*.f64 eh (cos.f64 t))

rewrite65.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

257×	`expm1-udef_binary64`
257×	`log1p-udef_binary64`
238×	`log-pow_binary64`
141×	`add-sqr-sqrt_binary64`
129×	`add-log-exp_binary64`

Counts

4 → 98

Calls

4 calls:

63.0ms	(*.f64 eh (cos.f64 t))
63.0ms	(*.f64 ew (sin.f64 t))
63.0ms	(/.f64 (/.f64 eh ew) (tan.f64 t))
63.0ms	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	270	34
2	3560	34
3	5030	34
0	0	0
1	0	0

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

567×	`fma-neg_binary64`
350×	`distribute-rgt-neg-in_binary64`
347×	`distribute-lft-neg-in_binary64`
242×	`neg-mul-1_binary64`
209×	`associate-r_binary64`

Counts

218 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	73	1411
1	209	1402
2	620	1382
3	1957	1378
4	4790	1378
5	4994	1378
6	4944	1378

prune132.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	170	5	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	171	5	176

Error

0.1b

Counts

176 → 5

Alt Table

Status	Error	Program
	31.4b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (sqrt.f64 (*.f64 eh (cos.f64 t))) 2) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (cbrt.f64 (*.f64 eh (cos.f64 t))) 3) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	18.8b	(fabs.f64 (fma.f64 (cbrt.f64 (pow.f64 (.f64 ew (sin.f64 t)) 3)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
▶	0.6b	(fabs.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 3) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	23.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (fma.f64 (.f64 eh (.f64 t t)) -1/2 eh) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 6048 to 1513 computations (75% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (cbrt.f64 (*.f64 ew (sin.f64 t))) 3)
	3.7b	(/.f64 (/.f64 eh ew) (tan.f64 t))
✓	7.0b	(cbrt.f64 (*.f64 ew (sin.f64 t)))
	35.2b	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

series710.0ms (5.2%)

Counts

2 → 48

Calls

2 calls:

361.0ms	(pow.f64 (cbrt.f64 (*.f64 ew (sin.f64 t))) 3)
349.0ms	(cbrt.f64 (*.f64 ew (sin.f64 t)))

rewrite80.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Counts

2 → 61

Calls

2 calls:

78.0ms	(pow.f64 (cbrt.f64 (*.f64 ew (sin.f64 t))) 3)
78.0ms	(cbrt.f64 (*.f64 ew (sin.f64 t)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	146	14
2	1576	14
3	4916	14
4	4901	14
0	0	0
1	0	0

simplify117.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

873×	`fma-neg_binary64`
531×	`distribute-rgt-neg-in_binary64`
470×	`unswap-sqr_binary64`
335×	`associate-r_binary64`
313×	`associate-l_binary64`

Counts

109 → 86

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1122
1	202	1054
2	580	934
3	2384	501
4	4897	501
5	4998	501
6	4934	501

prune218.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	212	6	218

Error

0.0b

Counts

218 → 6

Alt Table

Status	Error	Program
	0.7b	(fabs.f64 (fma.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 ew (sin.f64 t)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 ew (sin.f64 t))))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	31.4b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (sqrt.f64 (*.f64 eh (cos.f64 t))) 2) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (cbrt.f64 (*.f64 eh (cos.f64 t))) 3) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
▶	0.2b	(fabs.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 t) (/.f64 -1 ew))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.6b	(fabs.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 3) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	23.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (fma.f64 (.f64 eh (.f64 t t)) -1/2 eh) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 8111 to 2170 computations (73.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 eh (cos.f64 t))
✓	0.3b	(/.f64 (sin.f64 t) (/.f64 -1 ew))
	3.7b	(/.f64 (/.f64 eh ew) (tan.f64 t))
	35.2b	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(/.f64 (sin.f64 t) (/.f64 -1 ew))

rewrite73.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

674×	`log1p-expm1-u_binary64`
674×	`expm1-log1p-u_binary64`
254×	`prod-diff_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`

Counts

1 → 42

Calls

1 calls:

72.0ms

(/.f64 (sin.f64 t) (/.f64 -1 ew))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	146	8
2	1766	8
3	5000	8
4	5487	8
0	0	0
1	0	0

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1049×	`fma-neg_binary64`
817×	`cancel-sign-sub-inv_binary64`
438×	`fma-def_binary64`
396×	`distribute-rgt-neg-in_binary64`
337×	`distribute-lft-neg-in_binary64`

Counts

66 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	244
1	84	238
2	229	226
3	575	226
4	1810	226
5	3428	226
6	4760	226
7	4987	226
8	4896	226

prune243.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	203	6	209

Error

0.0b

Counts

209 → 6

Alt Table

Status	Error	Program
▶	0.7b	(fabs.f64 (fma.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 ew (sin.f64 t)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 ew (sin.f64 t))))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	31.4b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (sqrt.f64 (*.f64 eh (cos.f64 t))) 2) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (cbrt.f64 (*.f64 eh (cos.f64 t))) 3) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.2b	(fabs.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 t) (/.f64 -1 ew))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.6b	(fabs.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 3) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	23.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (fma.f64 (.f64 eh (.f64 t t)) -1/2 eh) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 7557 to 2386 computations (68.4% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (*.f64 ew (sin.f64 t))))
	3.7b	(/.f64 (/.f64 eh ew) (tan.f64 t))
	7.0b	(cbrt.f64 (*.f64 ew (sin.f64 t)))
	35.2b	(cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t))))

series949.0ms (7%)

Counts

1 → 24

Calls

1 calls:

949.0ms

(cbrt.f64 (cbrt.f64 (*.f64 ew (sin.f64 t))))

rewrite42.0ms (0.3%)

Algorithm

2×	batch-egg-rewrite

Rules

549×	`log1p-expm1-u_binary64`
549×	`expm1-log1p-u_binary64`
512×	`unpow-prod-down_binary64`
314×	`log-prod_binary64`
163×	`pow2_binary64`

Counts

1 → 53

Calls

1 calls:

41.0ms

(cbrt.f64 (cbrt.f64 (*.f64 ew (sin.f64 t))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	131	10
2	1468	10
3	5558	10
0	0	0
1	0	0

simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

792×	`distribute-rgt-neg-in_binary64`
637×	`distribute-lft-neg-in_binary64`
607×	`fma-def_binary64`
475×	`cancel-sign-sub-inv_binary64`
303×	`fma-neg_binary64`

Counts

77 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	530
1	137	530
2	310	482
3	1065	461
4	3093	413
5	4763	413
6	4991	413
7	4999	413
8	4899	413

prune485.0ms (3.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	373	0	373
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	373	6	379

Error

0.0b

Counts

379 → 6

Alt Table

Status	Error	Program
✓	0.7b	(fabs.f64 (fma.f64 (.f64 (.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 ew (sin.f64 t)))) 2)) (cbrt.f64 (cbrt.f64 (.f64 ew (sin.f64 t))))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	31.4b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (sqrt.f64 (*.f64 eh (cos.f64 t))) 2) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	0.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (pow.f64 (cbrt.f64 (*.f64 eh (cos.f64 t))) 3) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.2b	(fabs.f64 (fma.f64 (neg.f64 (/.f64 (sin.f64 t) (/.f64 -1 ew))) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
✓	0.6b	(fabs.f64 (fma.f64 (pow.f64 (cbrt.f64 (.f64 ew (sin.f64 t))) 3) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (*.f64 eh (cos.f64 t)) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))
	23.8b	(fabs.f64 (fma.f64 (.f64 ew (sin.f64 t)) (cos.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))) (.f64 (fma.f64 (.f64 eh (.f64 t t)) -1/2 eh) (sin.f64 (atan.f64 (/.f64 (/.f64 eh ew) (tan.f64 t)))))))

Compiler

Compiled 20039 to 5194 computations (74.1% saved)

regimes314.0ms (2.3%)

Accuracy

Total 0.0b remaining (39.1%)

Threshold costs 0.0b (39.1%)

Counts

41 → 1

Compiler

Compiled 6921 to 3974 computations (42.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

14×	`distribute-rgt-neg-in_binary64`
12×	`cancel-sign-sub-inv_binary64`
10×	`distribute-lft-neg-in_binary64`
8×	`distribute-lft-neg-out_binary64`
6×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	34	44
2	49	44
3	70	44
4	78	44
5	81	44
6	77	44

end140.0ms (1%)

Compiler: Compiled 275 to 150 computations (45.5% saved)

Details

analyze3.6s (26.5%)

sample5.9s (43.5%)

simplify7.0ms (0%)

prune3.0ms (0%)

localize18.0ms (0.1%)

series98.0ms (0.7%)

rewrite65.0ms (0.5%)

simplify97.0ms (0.7%)

prune132.0ms (1%)

localize22.0ms (0.2%)

series710.0ms (5.2%)

rewrite80.0ms (0.6%)

simplify117.0ms (0.9%)

prune218.0ms (1.6%)

localize22.0ms (0.2%)

series8.0ms (0.1%)

rewrite73.0ms (0.5%)

simplify87.0ms (0.6%)

prune243.0ms (1.8%)

localize28.0ms (0.2%)

series949.0ms (7%)

rewrite42.0ms (0.3%)

simplify114.0ms (0.8%)

prune485.0ms (3.6%)

regimes314.0ms (2.3%)

simplify5.0ms (0%)

end140.0ms (1%)

Profiling