Details

analyze2.6s (24%)

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
12.5%	87.4%	0.1%	7
12.5%	87.4%	0.1%	8
31.2%	68.6%	0.1%	9
31.2%	68.6%	0.1%	10
31.2%	68.6%	0.1%	11
40.6%	59.3%	0.1%	12
40.6%	59.3%	0.1%	13
40.6%	59.3%	0.1%	14

Compiler

Compiled 34 to 19 computations (44.1% saved)

sample5.5s (51.2%)

Results

2.9s	2005×	body	1024	valid
1.3s	4712×	body	128	valid
856.0ms	1011×	body	512	valid
293.0ms	523×	body	256	valid
18.0ms	5×	body	2048	valid

Compiler

Compiled 101 to 56 computations (44.6% saved)

simplify281.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1350×	`fma-def_binary64`
1306×	`fma-neg_binary64`
889×	`div-sub_binary64`
757×	`associate-/r/_binary64`
558×	`associate-/l*_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	44	50
2	109	50
3	229	50
4	333	50
5	515	50
6	717	50
7	984	50
8	1308	50
9	1633	50
10	1589	50
11	1591	50
12	1623	50
13	1671	50
14	1671	50
15	2103	50
16	2591	50
17	2559	50
18	2615	50
19	2783	50
20	2879	50
21	2927	50
22	3351	50
23	3319	50
24	3319	50
25	2487	50
26	2863	50
27	2591	50
28	2591	50
29	2591	50
30	2591	50
31	2376	50

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

0.1b

Counts

2 → 1

Alt Table

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

Status

Error

Program

▶

0.1b

(fabs.f64 (-.f64 (*.f64 (*.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (*.f64 (*.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 99 to 54 computations (45.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 ew (cos.f64 t))
✓	0.2b	(*.f64 (neg.f64 eh) (tan.f64 t))
✓	1.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	20.8b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))

series97.0ms (0.9%)

Counts

4 → 120

Calls

4 calls:

45.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
25.0ms	(*.f64 (neg.f64 eh) (tan.f64 t))
19.0ms	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))
7.0ms	(*.f64 ew (cos.f64 t))

rewrite65.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

630×	`log-prod_binary64`
217×	`expm1-udef_binary64`
217×	`log1p-udef_binary64`
199×	`log-pow_binary64`
131×	`add-sqr-sqrt_binary64`

Counts

4 → 116

Calls

4 calls:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	40
1	251	34
2	2959	34
3	5340	34
0	0	0
1	0	0

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

353×	`distribute-lft-neg-in_binary64`
348×	`distribute-rgt-neg-in_binary64`
314×	`fma-def_binary64`
273×	`neg-mul-1_binary64`
219×	`associate-/r/_binary64`

Counts

236 → 147

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1702
1	240	1696
2	769	1677
3	2558	1665
4	4808	1665
5	5075	1665

prune184.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	235	4	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	236	4	240

Error

0.1b

Counts

240 → 4

Alt Table

Status	Error	Program
	25.4b	(fabs.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 ew (cos.f64 t)) 3)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	34.7b	(fabs.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 ew (cos.f64 t))) 2) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
▶	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (/.f64 1 (hypot.f64 1 (/.f64 (.f64 eh (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	24.7b	(fabs.f64 (-.f64 (.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 8680 to 2242 computations (74.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (neg.f64 eh) (tan.f64 t))
✓	0.2b	(/.f64 1 (hypot.f64 1 (/.f64 (*.f64 eh (tan.f64 t)) ew)))
	1.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	1.6b	(/.f64 (*.f64 eh (tan.f64 t)) ew)

series238.0ms (2.2%)

Counts

2 → 72

Calls

2 calls:

195.0ms	(/.f64 1 (hypot.f64 1 (/.f64 (*.f64 eh (tan.f64 t)) ew)))
42.0ms	(/.f64 (*.f64 eh (tan.f64 t)) ew)

rewrite83.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

525×	`log-prod_binary64`
277×	`prod-diff_binary64`
189×	`pow1/3_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`

Counts

2 → 75

Calls

2 calls:

81.0ms	(/.f64 1 (hypot.f64 1 (/.f64 (*.f64 eh (tan.f64 t)) ew)))
81.0ms	(/.f64 (*.f64 eh (tan.f64 t)) ew)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	207	24
2	2550	24
3	4964	24
4	5533	24
0	0	0
1	0	0

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

457×	`associate-*r/_binary64`
382×	`associate-*l/_binary64`
328×	`fma-def_binary64`
260×	`associate-/r/_binary64`
231×	`cancel-sign-sub-inv_binary64`

Counts

147 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	140	2304
1	452	2264
2	1884	2219
3	5018	2219

prune217.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	205	4	209

Error

0.1b

Counts

209 → 4

Alt Table

Status	Error	Program
	25.4b	(fabs.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 ew (cos.f64 t)) 3)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	34.7b	(fabs.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 ew (cos.f64 t))) 2) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (/.f64 1 (hypot.f64 1 (/.f64 (.f64 eh (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
▶	24.7b	(fabs.f64 (-.f64 (.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 8463 to 3175 computations (62.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))
	1.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	8.4b	(.f64 ew (.f64 t t))
	20.8b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))

series61.0ms (0.6%)

Counts

2 → 60

Calls

2 calls:

53.0ms	(.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))
8.0ms	(.f64 ew (.f64 t t))

rewrite98.0ms (0.9%)

Algorithm

2×	batch-egg-rewrite

Rules

891×	`prod-diff_binary64`
269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
162×	`add-sqr-sqrt_binary64`
150×	`log1p-expm1-u_binary64`

Counts

2 → 35

Calls

2 calls:

97.0ms	(.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))
97.0ms	(.f64 ew (.f64 t t))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	35
1	317	32
2	3681	32
3	4894	32
4	6173	32
0	0	0
1	0	0

simplify190.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1652×	`fma-def_binary64`
829×	`fma-neg_binary64`
571×	`div-sub_binary64`
415×	`cancel-sign-sub-inv_binary64`
349×	`distribute-rgt-neg-in_binary64`

Counts

95 → 48

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	1692
1	94	1230
2	244	1164
3	646	1164
4	1011	1164
5	1935	1164
6	2335	1164
7	3293	1164
8	3634	1164
9	4021	1164
10	3917	1164
11	4721	1164
12	4915	1164
13	4818	1164

prune168.0ms (1.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	194	4	198

Error

0.1b

Counts

198 → 4

Alt Table

Status	Error	Program
▶	25.4b	(fabs.f64 (-.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 ew (cos.f64 t)) 3)) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	34.7b	(fabs.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 ew (cos.f64 t))) 2) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (/.f64 1 (hypot.f64 1 (/.f64 (.f64 eh (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	24.7b	(fabs.f64 (-.f64 (.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 7723 to 2156 computations (72.1% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (neg.f64 eh) (tan.f64 t))
	1.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
	20.8b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))
✓	36.9b	(cbrt.f64 (pow.f64 (*.f64 ew (cos.f64 t)) 3))

series15.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

15.0ms

(cbrt.f64 (pow.f64 (*.f64 ew (cos.f64 t)) 3))

rewrite67.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

603×	`log1p-expm1-u_binary64`
603×	`expm1-log1p-u_binary64`
328×	`log-prod_binary64`
121×	`expm1-udef_binary64`
121×	`log1p-udef_binary64`

Counts

1 → 32

Calls

1 calls:

66.0ms

(cbrt.f64 (pow.f64 (*.f64 ew (cos.f64 t)) 3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	6
1	147	6
2	1590	6
3	4931	6
4	4882	6
0	0	0
1	0	0

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

825×	`distribute-rgt-neg-in_binary64`
733×	`distribute-lft-neg-in_binary64`
502×	`associate-l_binary64`
436×	`associate-r_binary64`
420×	`neg-mul-1_binary64`

Counts

56 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	218
1	81	217
2	225	209
3	654	205
4	2584	205
5	4722	205
6	5066	205

prune212.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	251	2	253
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	252	5	257

Error

0.1b

Counts

257 → 5

Alt Table

Status	Error	Program
	37.7b	(fabs.f64 (-.f64 (.f64 (.f64 (sqrt.f64 ew) (.f64 (sqrt.f64 ew) (cos.f64 t))) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	17.9b	(fabs.f64 (-.f64 (.f64 (.f64 (cbrt.f64 (.f64 ew ew)) (.f64 (cbrt.f64 ew) (cos.f64 t))) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	34.7b	(fabs.f64 (-.f64 (.f64 (pow.f64 (sqrt.f64 (.f64 ew (cos.f64 t))) 2) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.1b	(fabs.f64 (-.f64 (.f64 (.f64 ew (cos.f64 t)) (/.f64 1 (hypot.f64 1 (/.f64 (.f64 eh (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	24.7b	(fabs.f64 (-.f64 (.f64 (fma.f64 (.f64 ew (.f64 t t)) -1/2 ew) (cos.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew)))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 9711 to 2986 computations (69.3% saved)

regimes267.0ms (2.5%)

Accuracy

Total 0.0b remaining (21.1%)

Threshold costs 0.0b (21.1%)

Counts

43 → 1

Compiler

Compiled 7524 to 4793 computations (36.3% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

19×	`*-commutative_binary64`
15×	`+-commutative_binary64`
15×	`sub-neg_binary64`
13×	`neg-sub0_binary64`
13×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	50
1	42	50
2	71	50
3	101	50
4	122	50
5	133	50
6	135	50
7	133	50

end123.0ms (1.1%)

Compiler: Compiled 251 to 152 computations (39.4% saved)

Details

analyze2.6s (24%)

sample5.5s (51.2%)

simplify281.0ms (2.6%)

prune2.0ms (0%)

localize19.0ms (0.2%)

series97.0ms (0.9%)

rewrite65.0ms (0.6%)

simplify92.0ms (0.9%)

prune184.0ms (1.7%)

localize22.0ms (0.2%)

series238.0ms (2.2%)

rewrite83.0ms (0.8%)

simplify61.0ms (0.6%)

prune217.0ms (2%)

localize21.0ms (0.2%)

series61.0ms (0.6%)

rewrite98.0ms (0.9%)

simplify190.0ms (1.8%)

prune168.0ms (1.6%)

localize23.0ms (0.2%)

series15.0ms (0.1%)

rewrite67.0ms (0.6%)

simplify68.0ms (0.6%)

prune212.0ms (2%)

regimes267.0ms (2.5%)

simplify4.0ms (0%)

end123.0ms (1.1%)

Profiling