Details

analyze200.0ms (8.2%)

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 22 to 17 computations (22.7% saved)

sample21.0ms (0.8%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify182.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

889×	`associate-/r*_binary64`
839×	`neg-mul-1_binary64`
735×	`sub-neg_binary64`
637×	`neg-sub0_binary64`
568×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	102	28
3	247	28
4	623	28
5	883	28
6	1301	28
7	2726	28
8	3095	28
9	3370	28
10	3431	28
11	3460	28
12	3552	28
13	4935	28
14	4948	28
15	4655	28
16	4895	28
17	4843	28

prune10.0ms (0.4%)

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

0.0b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 PI.f64) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Status

Error

Program

▶

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))

1.0b

(/.f64 4 (*.f64 (*.f64 (*.f64 3 PI.f64) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

Compiler

Compiled 99 to 74 computations (25.3% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
0.0b	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
0.2b	(.f64 (.f64 v v) 6)

rewrite153.0ms (6.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

25×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`associate-*r/_binary64`
18×	`flip3--_binary64` `sqrt-div_binary64` `flip--_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`pow1_binary64`

Counts

4 → 108

Calls

4 calls:

11.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
11.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
9.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
6.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 3262 to 2040 computations (37.5% saved)

series100.0ms (4.1%)

Error

Counts

4 → 21

Calls

4 calls:

31.0ms	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))
19.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
16.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
8.0ms	(.f64 (.f64 v v) 6)

Compiler

Compiled 1423 to 1209 computations (15% saved)

simplify137.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

428×	`distribute-rgt-in_binary64`
359×	`cancel-sign-sub-inv_binary64`
265×	`associate-r_binary64`
238×	`associate-l_binary64`
229×	`neg-mul-1_binary64`

Counts

129 → 111

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	3874
1	772	3457
2	3063	3412
3	4829	3412
4	5076	3412

prune121.0ms (5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	111	2	113

Error

Counts

113 → 2

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 4/3 (.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))
✓	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))

Status

Error

Program

▶

0.0b

(/.f64 4/3 (*.f64 PI.f64 (/.f64 (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))

✓

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))

Compiler

Compiled 2690 to 1828 computations (32% saved)

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (.f64 v v)))
0.0b	(.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v))))
0.0b	(/.f64 4/3 (.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))
0.2b	(.f64 6 (.f64 v v))

rewrite211.0ms (8.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

37×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`prod-exp_binary64` `add-cube-cbrt_binary64` `cbrt-unprod_binary64` `*-un-lft-identity_binary64`
11×	`pow1_binary64`
10×	`associate-r_binary64` `div-exp_binary64` `cbrt-undiv_binary64`

Counts

4 → 105

Calls

4 calls:

17.0ms	(/.f64 4/3 (.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))
16.0ms	(/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (.f64 v v)))
16.0ms	(.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v))))
6.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 3853 to 2610 computations (32.3% saved)

series108.0ms (4.5%)

Error

Counts

4 → 21

Calls

4 calls:

31.0ms	(/.f64 4/3 (.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))
23.0ms	(.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v))))
19.0ms	(/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (.f64 v v)))
10.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 1465 to 1244 computations (15.1% saved)

simplify156.0ms (6.4%)

Algorithm

1×	egg-herbie

Rules

283×	`times-frac_binary64`
271×	`associate-r_binary64`
253×	`cancel-sign-sub-inv_binary64` `associate-/l*_binary64`
241×	`associate-l_binary64`
190×	`associate-/r*_binary64`

Counts

126 → 101

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	4889
1	845	4011
2	3689	3952
3	4609	3952
4	5126	3952

prune108.0ms (4.4%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	101	2	103

Error

Counts

103 → 2

Alt Table

Status	Error	Program
	0.0b	(/.f64 4/3 (.f64 PI.f64 (/.f64 (.f64 (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))
	0.0b	(/.f64 4/3 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6))))))

Status

Error

Program

0.0b

(/.f64 4/3 (*.f64 PI.f64 (/.f64 (*.f64 (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v)))) (-.f64 1 (pow.f64 v 4))) (+.f64 1 (*.f64 v v)))))

0.0b

(/.f64 4/3 (*.f64 PI.f64 (*.f64 (-.f64 1 (*.f64 v v)) (sqrt.f64 (-.f64 2 (*.f64 (*.f64 v v) 6))))))

Compiler

Compiled 2662 to 1867 computations (29.9% saved)

regimes172.0ms (7.1%)

Accuracy

Total 0.0b remaining (17.1%)

Threshold costs 0.0b (17.1%)

Compiler

Compiled 3080 to 2340 computations (24% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`sub-neg_binary64` `+-commutative_binary64`
3×	`neg-mul-1_binary64` `neg-sub0_binary64` `cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
2×	`distribute-lft-neg-in_binary64`
1×	`1-exp_binary64` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	32	31
2	43	31
3	49	31
4	52	31
5	50	31

end1.0ms (0.1%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

sample720.0ms (29.7%)

Algorithm

1×

intervals

Results

428.0ms	8000×	body	128	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 88 to 67 computations (23.9% saved)

Details

analyze200.0ms (8.2%)

sample21.0ms (0.8%)

simplify182.0ms (7.5%)

prune10.0ms (0.4%)

localize10.0ms (0.4%)

rewrite153.0ms (6.3%)

series100.0ms (4.1%)

simplify137.0ms (5.7%)

prune121.0ms (5%)

localize14.0ms (0.6%)

rewrite211.0ms (8.7%)

series108.0ms (4.5%)

simplify156.0ms (6.4%)

prune108.0ms (4.4%)

regimes172.0ms (7.1%)

simplify4.0ms (0.2%)

end1.0ms (0.1%)

sample720.0ms (29.7%)

Profiling