Details

analyze94.0ms (2.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 21 to 16 computations (23.8% saved)

sample27.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 42 to 32 computations (23.8% saved)

simplify84.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

806×	`sub-neg_binary64`
743×	`div-sub_binary64`
502×	`associate-/l*_binary64`
427×	`unsub-neg_binary64`
423×	`distribute-rgt-in_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	37	29
2	82	29
3	187	29
4	471	29
5	845	29
6	1231	29
7	2569	29
8	2876	29
9	4256	29
10	5039	29

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	0	0
Done	0	0
Total	1	1

Error

0.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))

Compiler

Compiled 40 to 30 computations (25% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
0.0b	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
0.2b	(.f64 3 (.f64 v v))

rewrite205.0ms (5.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

38×	`add-sqr-sqrt_binary64`
26×	`associate-l_binary64`
22×	`times-frac_binary64`
22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`

Counts

3 → 114

Calls

3 calls:

17.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
11.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
4.0ms	(.f64 3 (.f64 v v))

Compiler

Compiled 3298 to 2324 computations (29.5% saved)

series44.0ms (1.2%)

Error

0.0b

Counts

3 → 15

Calls

3 calls:

12.0ms	(.f64 (.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (-.f64 1 (*.f64 v v)))
10.0ms	(.f64 (/.f64 (sqrt.f64 2) 4) (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v)))))
8.0ms	(.f64 3 (.f64 v v))

Compiler

Compiled 701 to 604 computations (13.8% saved)

simplify154.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

541×	`distribute-rgt-in_binary64`
496×	`distribute-lft-in_binary64`
349×	`associate-l_binary64`
329×	`associate-r_binary64`
238×	`cancel-sign-sub-inv_binary64`

Counts

129 → 83

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	249	3591
1	667	3304
2	2254	3284
3	4653	3284
4	4946	3284
5	4947	3284

prune64.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	2	84

Error

Counts

84 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))
▶	0.0b	(/.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9))))) (.f64 4 (sqrt.f64 (+.f64 1 (.f64 3 (*.f64 v v))))))

Status

Error

Program

1.0b

(*.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))

▶

0.0b

(/.f64 (*.f64 (-.f64 1 (*.f64 v v)) (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 v 4) 9))))) (*.f64 4 (sqrt.f64 (+.f64 1 (*.f64 3 (*.f64 v v))))))

Compiler

Compiled 1790 to 1353 computations (24.4% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9))))) (.f64 4 (sqrt.f64 (+.f64 1 (.f64 3 (*.f64 v v))))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9)))))
0.1b	(*.f64 (pow.f64 v 4) 9)
0.2b	(.f64 3 (.f64 v v))

rewrite154.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

40×	`add-exp-log_binary64`
37×	`add-cbrt-cube_binary64`
18×	`associate-*r/_binary64`
18×	`prod-exp_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

4 → 107

Calls

4 calls:

13.0ms	(/.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9))))) (.f64 4 (sqrt.f64 (+.f64 1 (.f64 3 (*.f64 v v))))))
9.0ms	(.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9)))))
5.0ms	(.f64 3 (.f64 v v))
5.0ms	(*.f64 (pow.f64 v 4) 9)

Compiler

Compiled 4303 to 3254 computations (24.4% saved)

series57.0ms (1.6%)

Error

Counts

4 → 18

Calls

4 calls:

14.0ms	(/.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9))))) (.f64 4 (sqrt.f64 (+.f64 1 (.f64 3 (*.f64 v v))))))
12.0ms	(.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9)))))
9.0ms	(*.f64 (pow.f64 v 4) 9)
7.0ms	(.f64 3 (.f64 v v))

Compiler

Compiled 993 to 850 computations (14.4% saved)

simplify100.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

488×	`distribute-rgt-in_binary64`
338×	`associate-r_binary64`
328×	`associate-l_binary64`
292×	`cancel-sign-sub-inv_binary64`
288×	`distribute-rgt-neg-in_binary64`

Counts

125 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	256	3764
1	673	3029
2	2911	2966
3	5020	2966

prune78.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
▶	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))
✓	0.0b	(/.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9))))) (.f64 4 (sqrt.f64 (+.f64 1 (.f64 3 (*.f64 v v))))))

Status

Error

Program

▶

1.0b

(*.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))

✓

0.0b

(/.f64 (*.f64 (-.f64 1 (*.f64 v v)) (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 v 4) 9))))) (*.f64 4 (sqrt.f64 (+.f64 1 (*.f64 3 (*.f64 v v))))))

Compiler

Compiled 2565 to 1954 computations (23.8% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))
0.2b	(.f64 3 (.f64 v v))
0.2b	(.f64 3 (.f64 v v))
1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)))

rewrite413.0ms (11.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

384×	`sqrt-div_binary64`
266×	`frac-times_binary64`
151×	`associate-*l/_binary64`
132×	`flip--_binary64`
132×	`flip3--_binary64`

Counts

4 → 268

Calls

4 calls:

37.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))
28.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)))
5.0ms	(.f64 3 (.f64 v v))
4.0ms	(.f64 3 (.f64 v v))

Compiler

Compiled 17050 to 12348 computations (27.6% saved)

series120.0ms (3.3%)

Error

Counts

4 → 18

Calls

4 calls:

80.0ms	(.f64 3 (.f64 v v))
13.0ms	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))
11.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)))
7.0ms	(.f64 3 (.f64 v v))

Compiler

Compiled 1092 to 931 computations (14.7% saved)

simplify417.0ms (11.4%)

Algorithm

1×	egg-herbie

Rules

696×	`*-commutative_binary64`
515×	`associate-/l*_binary64`
365×	`distribute-rgt-in_binary64`
364×	`distribute-lft-in_binary64`
246×	`associate-l_binary64`

Counts

286 → 270

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	441	15796
1	1248	12573
2	3119	12145
3	4601	11995
4	4974	11995

prune194.0ms (5.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	270	0	270
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	270	2	272

Error

Counts

272 → 2

Alt Table

Status	Error	Program
	1.0b	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (.f64 3 (.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))
	0.0b	(/.f64 (.f64 (-.f64 1 (.f64 v v)) (.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (.f64 (pow.f64 v 4) 9))))) (.f64 4 (sqrt.f64 (+.f64 1 (.f64 3 (*.f64 v v))))))

Status

Error

Program

1.0b

(*.f64 (*.f64 (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2)) (*.f64 (sqrt.f64 (sqrt.f64 (-.f64 1 (*.f64 3 (*.f64 v v))))) (/.f64 (sqrt.f64 (sqrt.f64 2)) 2))) (-.f64 1 (*.f64 v v)))

0.0b

(/.f64 (*.f64 (-.f64 1 (*.f64 v v)) (*.f64 (sqrt.f64 2) (sqrt.f64 (-.f64 1 (*.f64 (pow.f64 v 4) 9))))) (*.f64 4 (sqrt.f64 (+.f64 1 (*.f64 3 (*.f64 v v))))))

Compiler

Compiled 6028 to 4586 computations (23.9% saved)

regimes434.0ms (11.9%)

Accuracy

Total 0.0b remaining (22.8%)

Threshold costs 0.0b (22.8%)

Compiler

Compiled 10405 to 8233 computations (20.9% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
7×	`*-commutative_binary64`
6×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	38
1	31	38
2	47	38
3	55	38
4	60	38
5	61	38
6	59	38

end1.0ms (0%)

Compiler: Compiled 26 to 20 computations (23.1% saved)

sample956.0ms (26.2%)

Algorithm

1×

intervals

Results

695.0ms

8000×

body

128

valid

Compiler

Compiled 115 to 90 computations (21.7% saved)

Details

analyze94.0ms (2.6%)

sample27.0ms (0.7%)

simplify84.0ms (2.3%)

prune2.0ms (0%)

localize11.0ms (0.3%)

rewrite205.0ms (5.6%)

series44.0ms (1.2%)

simplify154.0ms (4.2%)

prune64.0ms (1.8%)

localize18.0ms (0.5%)

rewrite154.0ms (4.2%)

series57.0ms (1.6%)

simplify100.0ms (2.7%)

prune78.0ms (2.1%)

localize14.0ms (0.4%)

rewrite413.0ms (11.3%)

series120.0ms (3.3%)

simplify417.0ms (11.4%)

prune194.0ms (5.3%)

regimes434.0ms (11.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample956.0ms (26.2%)

Profiling