Details

analyze140.0ms (2.9%)

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%	50%	50%	4
0%	50%	50%	5
12.5%	37.5%	50%	6
18.7%	31.2%	50%	7
28.1%	21.9%	50%	8
32.8%	17.2%	50%	9
38.2%	11.7%	50%	10
41%	9%	50%	11
43.9%	6%	50%	12
45.4%	4.6%	50%	13
46.9%	3.1%	50%	14

Compiler

Compiled 31 to 22 computations (29% saved)

sample59.0ms (1.2%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 63 to 45 computations (28.6% saved)

simplify32.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

826×	`times-frac_binary64`
592×	`fma-def_binary64`
509×	`associate-/r*_binary64`
353×	`associate-/l*_binary64`
343×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	43
1	58	43
2	179	38
3	824	36
4	3882	36
5	5029	36

prune4.0ms (0.1%)

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

0.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 106 to 73 computations (31.1% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
✓	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.5b	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

series197.0ms (4%)

Counts

4 → 72

Calls

4 calls:

139.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
41.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
14.0ms	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
2.0ms	(*.f64 (PI.f64) t)

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

4 → 131

Calls

4 calls:

17.0ms	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
11.0ms	(.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
6.0ms	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
3.0ms	(*.f64 (PI.f64) t)

simplify116.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

563×	`associate-r_binary64`
513×	`associate-l_binary64`
460×	`associate-/r*_binary64`
416×	`times-frac_binary64`
245×	`associate-/l*_binary64`

Counts

203 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	444	7617
1	1247	6841
2	5223	6841

prune233.0ms (4.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	221	5	226
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	221	6	227

Error

Counts

227 → 6

Alt Table

Status	Error	Program
	1.0b	(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
	1.1b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
▶	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
	0.5b	(.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 9451 to 5858 computations (38% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
	0.3b	(*.f64 (PI.f64) t)
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
✓	1.0b	(/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)))

series147.0ms (3%)

Counts

2 → 36

Calls

2 calls:

133.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

14.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`times-frac_binary64`
43×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
43×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

2 → 113

Calls

2 calls:

9.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

3.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

simplify150.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

879×	`fma-def_binary64`
419×	`associate-/r*_binary64`
279×	`times-frac_binary64`
276×	`associate-/l*_binary64`
250×	`associate-l_binary64`

Counts

149 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	436	7537
1	1236	6895
2	4807	6872
3	5527	6872

prune300.0ms (6.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	289	6	295

Error

Counts

295 → 6

Alt Table

Status	Error	Program
	1.0b	(/.f64 (sqrt.f64 1/2) (*.f64 (PI.f64) t))
	1.1b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
	0.6b	(.f64 (/.f64 (-.f64 1 (.f64 5 (pow.f64 v 2))) (.f64 (-.f64 (PI.f64) (.f64 (pow.f64 v 2) (PI.f64))) t)) (sqrt.f64 (/.f64 1 (-.f64 2 (*.f64 6 (pow.f64 v 2))))))
▶	0.5b	(.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))

Compiler

Compiled 12123 to 7960 computations (34.3% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (PI.f64) t)
✓	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))
✓	0.4b	(.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	1.0b	(/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

series204.0ms (4.2%)

Counts

3 → 60

Calls

3 calls:

135.0ms

(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))

59.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

9.0ms

(/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

rewrite38.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-exp-log_binary64`
47×	`add-sqr-sqrt_binary64`
46×	`times-frac_binary64`
46×	`add-cbrt-cube_binary64`
37×	`*-un-lft-identity_binary64`

Counts

3 → 148

Calls

3 calls:

13.0ms

(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2))) (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))))

6.0ms

(/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))

4.0ms

(/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

simplify157.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

529×	`fma-def_binary64`
456×	`associate-/r*_binary64`
401×	`times-frac_binary64`
333×	`associate-r_binary64`
305×	`associate-l_binary64`

Counts

208 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	450	8471
1	1270	7502
2	4739	7480
3	4970	7480

prune299.0ms (6.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	2	1	3
Picked	1	0	1
Done	0	2	2
Total	287	5	292

Error

Counts

292 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (pow.f64 (fma.f64 v (.f64 -6 v) 2) -1/2) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	1.1b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
▶	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

Compiler

Compiled 11930 to 7935 computations (33.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))
	0.3b	(*.f64 (PI.f64) t)
	0.3b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))
✓	0.5b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

series137.0ms (2.8%)

Counts

1 → 24

Calls

1 calls:

137.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`times-frac_binary64`
35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`

Counts

1 → 90

Calls

1 calls:

12.0ms

(/.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (*.f64 (*.f64 (PI.f64) t) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

simplify147.0ms (3%)

Algorithm

1×	egg-herbie

Rules

941×	`fma-def_binary64`
368×	`associate-/r*_binary64`
284×	`associate-r_binary64`
279×	`times-frac_binary64`
217×	`associate-l_binary64`

Counts

114 → 163

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	382	6976
1	1034	6467
2	4292	6452
3	5063	6452

prune287.0ms (5.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	282	0	282
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	282	5	287

Error

Counts

287 → 5

Alt Table

Status	Error	Program
	0.6b	(.f64 (pow.f64 (fma.f64 v (.f64 -6 v) 2) -1/2) (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
✓	0.4b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (fma.f64 v (.f64 -6 v) 2)) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))))
	1.1b	(/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (sqrt.f64 (.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)) (cbrt.f64 (fma.f64 v (.f64 -6 v) 2)))) (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v))))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (sqrt.f64 (fma.f64 v (.f64 -6 v) 2))) (.f64 (.f64 (PI.f64) t) (-.f64 1 (*.f64 v v))))
✓	0.4b	(/.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (.f64 (.f64 (PI.f64) t) (-.f64 1 (.f64 v v)))) (sqrt.f64 (fma.f64 v (*.f64 -6 v) 2)))

Compiler

Compiled 11548 to 7232 computations (37.4% saved)

regimes974.0ms (20%)

Accuracy

Total 0.3b remaining (82.4%)

Threshold costs 0.3b (82.4%)

Counts

101 → 1

Compiler

Compiled 20388 to 14990 computations (26.5% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`
8×	`+-commutative_binary64`
8×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	53
1	39	53
2	59	53
3	71	53
4	80	53
5	83	53
6	81	53

end1.0ms (0%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

sample1.1s (22.5%)

Algorithm

1×

intervals

Results

709.0ms	8000×	body	128	valid
1.0ms	11×	body	128	nan

Compiler

Compiled 218 to 163 computations (25.2% saved)

Details

analyze140.0ms (2.9%)

sample59.0ms (1.2%)

simplify32.0ms (0.7%)

prune4.0ms (0.1%)

localize14.0ms (0.3%)

series197.0ms (4%)

rewrite47.0ms (1%)

simplify116.0ms (2.4%)

prune233.0ms (4.8%)

localize15.0ms (0.3%)

series147.0ms (3%)

rewrite25.0ms (0.5%)

simplify150.0ms (3.1%)

prune300.0ms (6.2%)

localize15.0ms (0.3%)

series204.0ms (4.2%)

rewrite38.0ms (0.8%)

simplify157.0ms (3.2%)

prune299.0ms (6.1%)

localize16.0ms (0.3%)

series137.0ms (2.8%)

rewrite26.0ms (0.5%)

simplify147.0ms (3%)

prune287.0ms (5.9%)

regimes974.0ms (20%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.1s (22.5%)

Profiling