Details

sample40.0ms

Algorithm

intervals

Results

15.0ms	265×	body	80	nan
13.0ms	256×	body	80	valid

simplify63.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	10
1	91	10
2	275	10
3	672	10
4	1303	10
5	1737	10
6	1802	10
7	1802	10

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

Merged error: 1.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.2b	(* 6.0 (* v v))
1.0b	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
18×	`associate-*r/` `prod-exp` `cbrt-unprod`
14×	`add-sqr-sqrt`
13×	`flip3--` `flip--`
12×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div` `pow-prod-down`
11×	`associate-r`
8×	`frac-times` `associate-/r/`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `sqrt-prod` `-commutative` `associate-/l`
2×	`sub-neg`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

7.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
11.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms	(* 6.0 (* v v))
12.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series811.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
262.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
24.0ms	(* 6.0 (* v v))
420.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify115.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	955	1468
1	4696	1282
2	5001	1281

prune279.0ms

Filtered

135 candidates to 89 candidates (65.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Merged error: 0b

Counts

136 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 2.0 (* 6.0 (* v v)))
0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.0b	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
0.2b	(* 6.0 (* v v))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log` `add-cbrt-cube`
14×	`pow1` `add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`prod-diff` `prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-r`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `log1p-expm1-u`
3×	`cbrt-undiv` `sub-neg` `flip3--` `times-frac` `fma-neg` `div-exp` `flip--` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/r*` `div-inv` `difference-of-squares` `unswap-sqr`

Counts

4 → 101

Calls

4 calls:

4.0ms	(- 2.0 (* 6.0 (* v v)))
7.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
11.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms	(* 6.0 (* v v))

series293.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- 2.0 (* 6.0 (* v v)))
105.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
101.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
25.0ms	(* 6.0 (* v v))

simplify66.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	545	701
1	2488	597
2	5002	594

prune201.0ms

Filtered

113 candidates to 73 candidates (64.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	114	1	115

Merged error: 0b

Counts

115 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
0.1b	(pow (* 6.0 (* v v)) 3)
0.2b	(* 6.0 (* v v))
19.5b	(cbrt (pow (* 6.0 (* v v)) 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
8×	`cbrt-prod`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `pow-pow` `times-frac` `div-exp` `associate-l` `pow-exp` `associate-/l*` `rem-cube-cbrt`
2×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod` `associate-*r/` `associate-/r/` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `associate-r` `clear-num` `associate-/r` `-commutative` `flip--` `rem-cbrt-cube` `div-inv` `unswap-sqr`

Counts

4 → 94

Calls

4 calls:

7.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms	(pow (* 6.0 (* v v)) 3)
6.0ms	(* 6.0 (* v v))
3.0ms	(cbrt (pow (* 6.0 (* v v)) 3))

series201.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
52.0ms	(pow (* 6.0 (* v v)) 3)
24.0ms	(* 6.0 (* v v))
25.0ms	(cbrt (pow (* 6.0 (* v v)) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	430	495
1	1998	438
2	5001	437

prune228.0ms

Filtered

106 candidates to 70 candidates (66.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	1	107

Merged error: 0b

Counts

107 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample967.0ms

Algorithm

intervals

Results

396.0ms	8000×	body	80	valid
377.0ms	8014×	body	80	nan