Details

analyze2.3s (20.6%)

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 (48.6%)

Results

3.0s	2083×	body	1024	valid
1.2s	4575×	body	128	valid
915.0ms	1056×	body	512	valid
303.0ms	530×	body	256	valid
39.0ms	12×	body	2048	valid

Compiler

Compiled 68 to 38 computations (44.1% saved)

preprocess51.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

946×	`fma-def_binary64`
468×	`fma-neg_binary64`
352×	`times-frac_binary64`
303×	`cancel-sign-sub-inv_binary64`
212×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	200
1	152	200
2	439	200
3	1107	200
4	1793	200
5	3387	200
6	4384	200
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 33 to 18 computations (45.5% saved)

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1286×	`fma-def_binary64`
698×	`fma-neg_binary64`
423×	`times-frac_binary64`
245×	`div-sub_binary64`
182×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	44	50
2	118	50
3	290	50
4	456	50
5	801	50
6	1325	50
7	2149	50
8	3160	50
9	4423	50
10	4992	50

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

3 → 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 129 to 64 computations (50.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 ew (cos.f64 t)) (cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))
✓	0.2b	(*.f64 (neg.f64 eh) (tan.f64 t))
✓	2.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	24.6b	(cos.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)))

series120.0ms (1.1%)

Counts

4 → 132

Calls

33 calls:

6.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)	ew	0
6.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)	eh	inf
5.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)	eh	0
5.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)	t	-inf
5.0ms	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)	t	inf

rewrite61.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

237×	`expm1-udef_binary64`
237×	`log1p-udef_binary64`
142×	`add-sqr-sqrt_binary64`
140×	`*-un-lft-identity_binary64`
140×	`pow1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	57
1	273	48
2	3730	48

Stop Event

1×	node limit

Counts

4 → 105

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

474×	`distribute-lft-neg-in_binary64`
472×	`distribute-rgt-neg-in_binary64`
351×	`fma-def_binary64`
300×	`associate-l_binary64`
272×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	82	2488
1	255	2428
2	887	2378
3	3738	2378

Stop Event

1×	node limit

Counts

237 → 137

prune160.0ms (1.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	220	3	223
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	221	3	224

Error

0.1b

Counts

224 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (-.f64 (.f64 (cos.f64 t) (.f64 (cos.f64 (atan.f64 (.f64 -1 (/.f64 (.f64 (tan.f64 t) eh) ew)))) ew)) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	24.5b	(fabs.f64 (-.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 2) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	0.8b	(fabs.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 8004 to 2199 computations (72.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 (neg.f64 eh) (tan.f64 t))
	2.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	2.6b	(/.f64 (*.f64 (tan.f64 t) eh) ew)
✓	24.6b	(cos.f64 (atan.f64 (.f64 -1 (/.f64 (.f64 (tan.f64 t) eh) ew))))

series59.0ms (0.5%)

Counts

2 → 36

Calls

18 calls:

6.0ms	(/.f64 (*.f64 (tan.f64 t) eh) ew)	eh	0
6.0ms	(/.f64 (*.f64 (tan.f64 t) eh) ew)	ew	-inf
5.0ms	(/.f64 (*.f64 (tan.f64 t) eh) ew)	eh	-inf
5.0ms	(/.f64 (*.f64 (tan.f64 t) eh) ew)	t	-inf
5.0ms	(/.f64 (*.f64 (tan.f64 t) eh) ew)	t	inf

rewrite50.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

553×	`log-prod_binary64`
192×	`expm1-udef_binary64`
192×	`log1p-udef_binary64`
162×	`log-pow_binary64`
116×	`log-div_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	226	22
2	2975	22

Stop Event

1×	node limit

Counts

2 → 89

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
549×	`associate-/l*_binary64`
420×	`associate-/r*_binary64`
414×	`associate-/r/_binary64`
338×	`*-commutative_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	34	556
1	90	554
2	235	554
3	607	551
4	1809	539
5	4607	530

Stop Event

1×	node limit

Counts

125 → 99

prune207.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	185	0	185
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	185	3	188

Error

0.1b

Counts

188 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fabs.f64 (-.f64 (.f64 (cos.f64 t) (.f64 (cos.f64 (atan.f64 (.f64 -1 (/.f64 (.f64 (tan.f64 t) eh) ew)))) ew)) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	24.5b	(fabs.f64 (-.f64 (pow.f64 (sqrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 2) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
▶	0.8b	(fabs.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 6893 to 2569 computations (62.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3)
✓	2.3b	(*.f64 (/.f64 eh ew) (tan.f64 t))
	2.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)
✓	10.5b	(cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t)))))

series994.0ms (8.8%)

Counts

3 → 68

Calls

27 calls:

189.0ms	(pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3)	t	inf
168.0ms	(pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3)	t	-inf
151.0ms	(cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t)))))	t	inf
150.0ms	(cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t)))))	t	-inf
56.0ms	(pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3)	ew	-inf

rewrite66.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`expm1-udef_binary64`
256×	`log1p-udef_binary64`
147×	`add-sqr-sqrt_binary64`
142×	`pow1_binary64`
140×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	316	51
2	3851	51

Stop Event

1×	node limit

Counts

3 → 126

simplify57.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

367×	`cancel-sign-sub-inv_binary64`
315×	`unswap-sqr_binary64`
193×	`associate-r_binary64`
174×	`associate-/r/_binary64`
167×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	2253
1	649	2184
2	2595	2155

Stop Event

1×	node limit

Counts

194 → 171

prune260.0ms (2.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	223	4	227
Fresh	1	0	1
Picked	0	1	1
Done	1	0	1
Total	225	5	230

Error

0.1b

Counts

230 → 5

Alt Table

Status	Error	Program
▶	0.1b	(fabs.f64 (-.f64 (/.f64 ew (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	0.9b	(fabs.f64 (-.f64 (pow.f64 (/.f64 (cbrt.f64 ew) (cbrt.f64 (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t)))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	0.2b	(fabs.f64 (-.f64 (/.f64 (cos.f64 t) (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) ew)) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	1.0b	(fabs.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) (.f64 ew (cos.f64 t))))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.8b	(fabs.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 9582 to 3696 computations (61.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (hypot.f64 1 (*.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))
	0.2b	(*.f64 (neg.f64 eh) (tan.f64 t))
	2.3b	(*.f64 (/.f64 eh ew) (tan.f64 t))
	2.6b	(/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew)

series73.0ms (0.6%)

Counts

1 → 36

Calls

9 calls:

16.0ms	(/.f64 (hypot.f64 1 (*.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))	t	-inf
16.0ms	(/.f64 (hypot.f64 1 (*.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))	t	inf
7.0ms	(/.f64 (hypot.f64 1 (*.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))	ew	-inf
6.0ms	(/.f64 (hypot.f64 1 (*.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))	eh	-inf
6.0ms	(/.f64 (hypot.f64 1 (*.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))	t	0

rewrite46.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

584×	`log-prod_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
177×	`log-pow_binary64`
136×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	225	17
2	2945	17

Stop Event

1×	node limit

Counts

1 → 36

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-l_binary64`
404×	`fma-def_binary64`
401×	`associate-*r/_binary64`
361×	`associate-*l/_binary64`
213×	`associate-/r/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	125	1771
1	416	1707
2	1838	1669

Stop Event

1×	node limit

Counts

72 → 68

prune297.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	195	2	197
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	196	6	202

Error

0.1b

Counts

202 → 6

Alt Table

Status	Error	Program
	0.2b	(fabs.f64 (-.f64 (/.f64 (cos.f64 t) (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) ew)) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	0.2b	(fabs.f64 (-.f64 (/.f64 ew (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 1 (/.f64 eh (/.f64 ew (tan.f64 t)))) (cos.f64 t)) 3))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	0.4b	(fabs.f64 (-.f64 (/.f64 ew (pow.f64 (cbrt.f64 (/.f64 (hypot.f64 1 (/.f64 eh (/.f64 ew (tan.f64 t)))) (cos.f64 t))) 3)) (.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 ew (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) (cos.f64 t))) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
	1.0b	(fabs.f64 (-.f64 (pow.f64 (/.f64 1 (cbrt.f64 (/.f64 (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))) (.f64 ew (cos.f64 t))))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))
✓	0.8b	(fabs.f64 (-.f64 (pow.f64 (cbrt.f64 (/.f64 (.f64 ew (cos.f64 t)) (hypot.f64 1 (.f64 (/.f64 eh ew) (tan.f64 t))))) 3) (.f64 (.f64 eh (sin.f64 t)) (sin.f64 (atan.f64 (/.f64 (*.f64 (neg.f64 eh) (tan.f64 t)) ew))))))

Compiler

Compiled 7649 to 2922 computations (61.8% saved)

regimes510.0ms (4.5%)

Accuracy

Total 0.0b remaining (28.3%)

Threshold costs 0.0b (28.3%)

Counts

64 → 1

Compiler

Compiled 10544 to 7093 computations (32.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	50
1	44	50
2	76	50
3	105	50
4	125	50
5	135	50
6	137	50

Stop Event

1×

saturated

end168.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 272 to 176 computations (35.3% saved)

Details

analyze2.3s (20.6%)

sample5.5s (48.6%)

preprocess51.0ms (0.5%)

simplify39.0ms (0.3%)

prune3.0ms (0%)

localize19.0ms (0.2%)

series120.0ms (1.1%)

rewrite61.0ms (0.5%)

simplify72.0ms (0.6%)

prune160.0ms (1.4%)

localize24.0ms (0.2%)

series59.0ms (0.5%)

rewrite50.0ms (0.4%)

simplify39.0ms (0.3%)

prune207.0ms (1.8%)

localize26.0ms (0.2%)

series994.0ms (8.8%)

rewrite66.0ms (0.6%)

simplify57.0ms (0.5%)

prune260.0ms (2.3%)

localize22.0ms (0.2%)

series73.0ms (0.6%)

rewrite46.0ms (0.4%)

simplify45.0ms (0.4%)

prune297.0ms (2.6%)

regimes510.0ms (4.5%)

simplify5.0ms (0%)

end168.0ms (1.5%)

Profiling