Details

sample41.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
13.0ms	265×	body	80	nan

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	10
1	91	10
2	263	10
3	620	10
4	1138	10
5	1470	10
6	1510	10
7	1510	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

localize12.0ms

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))))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

6.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
11.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
5.0ms	(* 6.0 (* v v))
12.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series840.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
276.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
24.0ms	(* 6.0 (* v v))
426.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	888	1350
1	4408	1176
2	5002	1174

prune250.0ms

Filtered

121 candidates to 78 candidates (64.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	2	122

Merged error: 0b

Counts

122 → 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))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

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

series297.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- 2.0 (* 6.0 (* v v)))
106.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
106.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
25.0ms	(* 6.0 (* v v))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	473	552
1	2214	464
2	5001	464

prune155.0ms

Filtered

93 candidates to 59 candidates (63.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	94	1	95

Merged error: 0b

Counts

95 → 1

localize14.0ms

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))

rewrite23.0ms

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×	`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 → 86

Calls

4 calls:

7.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms	(pow (* 6.0 (* v v)) 3)
5.0ms	(* 6.0 (* v v))
3.0ms	(cbrt (pow (* 6.0 (* v v)) 3))

series209.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
53.0ms	(pow (* 6.0 (* v v)) 3)
24.0ms	(* 6.0 (* v v))
30.0ms	(cbrt (pow (* 6.0 (* v v)) 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	417	464
1	1967	406
2	5002	406

prune199.0ms

Filtered

98 candidates to 62 candidates (63.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	98	1	99

Merged error: 0b

Counts

99 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample990.0ms

Algorithm

intervals

Results

401.0ms	8000×	body	80	valid
392.0ms	8014×	body	80	nan