Details

analyze205.0ms (7%)

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)

sample19.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify180.0ms (6.2%)

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

prune6.0ms (0.2%)

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
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 PI.f64) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.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

1.0b

(/.f64 4 (*.f64 (*.f64 (*.f64 3 PI.f64) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.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 99 to 74 computations (25.3% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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))))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (.f64 v v) 6))))
0.1b	(.f64 (.f64 v v) 6)

rewrite163.0ms (5.6%)

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:

14.0ms	(.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 (*.f64 v v) 6)))))
11.0ms	(/.f64 4/3 (.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)

series94.0ms (3.2%)

Error

0.0b

Counts

4 → 21

Calls

4 calls:

29.0ms	(/.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)

simplify140.0ms (4.8%)

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 → 108

Iterations

Useful iterations: 2 (0.0ms)

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

prune105.0ms (3.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Error

Counts

110 → 2

Alt Table

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

Status

Error

Program

0.0b

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

▶

0.0b

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

Compiler

Compiled 2671 to 1816 computations (32% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 4/3 (/.f64 1 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))))
0.0b	(/.f64 1 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (*.f64 v v)))))))
0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
0.1b	(.f64 6 (.f64 v v))

rewrite214.0ms (7.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

64×	`add-exp-log_binary64`
34×	`add-cbrt-cube_binary64`
32×	`prod-exp_binary64`
23×	`associate-*r/_binary64`
22×	`associate-r_binary64`

Counts

4 → 136

Calls

4 calls:

16.0ms	(.f64 4/3 (/.f64 1 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))))
12.0ms	(/.f64 1 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (*.f64 v v)))))))
11.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
6.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 4204 to 2756 computations (34.4% saved)

series103.0ms (3.5%)

Error

Counts

4 → 21

Calls

4 calls:

27.0ms	(.f64 4/3 (/.f64 1 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))))
25.0ms	(/.f64 1 (.f64 PI.f64 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (*.f64 v v)))))))
17.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
8.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 1547 to 1321 computations (14.6% saved)

simplify162.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

406×	`distribute-rgt-in_binary64`
308×	`cancel-sign-sub-inv_binary64`
273×	`associate-r_binary64`
224×	`neg-mul-1_binary64`
203×	`associate-/r*_binary64`

Counts

157 → 112

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	325	4783
1	819	4195
2	3198	4133
3	4838	4133
4	5051	4133

prune96.0ms (3.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Error

Counts

114 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

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

✓

0.0b

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

Compiler

Compiled 2383 to 1678 computations (29.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
0.1b	(.f64 6 (.f64 v v))
1.0b	(/.f64 4/3 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
1.0b	(.f64 (/.f64 1 PI.f64) (/.f64 4/3 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (*.f64 v v)))))))

rewrite217.0ms (7.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

55×	`add-exp-log_binary64`
37×	`add-cbrt-cube_binary64`
32×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
21×	`prod-exp_binary64` `-un-lft-identity_binary64` `associate-l*_binary64`

Counts

4 → 141

Calls

4 calls:

17.0ms	(.f64 (/.f64 1 PI.f64) (/.f64 4/3 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (*.f64 v v)))))))
9.0ms	(/.f64 4/3 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
9.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
5.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 4517 to 2969 computations (34.3% saved)

series104.0ms (3.6%)

Error

Counts

4 → 21

Calls

4 calls:

29.0ms	(.f64 (/.f64 1 PI.f64) (/.f64 4/3 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (*.f64 v v)))))))
23.0ms	(/.f64 4/3 (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
17.0ms	(.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
10.0ms	(.f64 6 (.f64 v v))

Compiler

Compiled 1531 to 1338 computations (12.6% saved)

simplify165.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

321×	`cancel-sign-sub-inv_binary64`
256×	`associate-r_binary64`
243×	`distribute-rgt-in_binary64`
236×	`times-frac_binary64`
212×	`associate-l_binary64`

Counts

162 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	5085
1	869	4415
2	3407	4360
3	4781	4360
4	5037	4360

prune131.0ms (4.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	145	2	147

Error

Counts

147 → 2

Alt Table

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

Status

Error

Program

0.0b

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

0.0b

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

Compiler

Compiled 3390 to 2339 computations (31% saved)

regimes117.0ms (4%)

Accuracy

Total 0.0b remaining (29.4%)

Threshold costs 0.0b (29.4%)

Compiler

Compiled 1666 to 1302 computations (21.8% saved)

simplify4.0ms (0.1%)

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%)

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

sample674.0ms (23%)

Algorithm

1×

intervals

Results

407.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 86 to 66 computations (23.3% saved)

Details

analyze205.0ms (7%)

sample19.0ms (0.7%)

simplify180.0ms (6.2%)

prune6.0ms (0.2%)

localize10.0ms (0.3%)

rewrite163.0ms (5.6%)

series94.0ms (3.2%)

simplify140.0ms (4.8%)

prune105.0ms (3.6%)

localize11.0ms (0.4%)

rewrite214.0ms (7.3%)

series103.0ms (3.5%)

simplify162.0ms (5.5%)

prune96.0ms (3.3%)

localize11.0ms (0.4%)

rewrite217.0ms (7.4%)

series104.0ms (3.6%)

simplify165.0ms (5.6%)

prune131.0ms (4.5%)

regimes117.0ms (4%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample674.0ms (23%)

Profiling