Details

sample52.0ms

Algorithm

intervals

Results

20.0ms	289×	body	80	nan
19.0ms	256×	body	80	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

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)))))
0.1b	(* 6.0 (* v v))
1.0b	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

rewrite80.0ms

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:

10.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
30.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms	(* 6.0 (* v v))
30.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
17.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
2.0ms	(* 6.0 (* v v))
20.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify104.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (92.0ms)

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

prune796.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 3.0 PI) (- 1.0 (* v v)))
0.1b	(* 6.0 (* v v))
1.0b	(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b	(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-exp-log`
48×	`add-cbrt-cube`
46×	`add-sqr-sqrt`
44×	`prod-exp`
41×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
29×	`associate-r`
23×	`div-exp`
22×	`sqrt-prod`
20×	`cbrt-unprod`
16×	`pow1`
13×	`associate-l`
11×	`cbrt-undiv`
7×	`pow-prod-down`
6×	`rec-exp` `1-exp` `associate-/r*` `associate-/r/`
5×	`associate-*r/`
4×	`flip3--` `sqrt-div` `flip--` `add-log-exp` `unswap-sqr`
3×	`-commutative` `div-inv` `associate-/l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `difference-of-squares`

Counts

4 → 161

Calls

4 calls:

11.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
6.0ms	(* 6.0 (* v v))
64.0ms	(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
6.0ms	(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
2.0ms	(* 6.0 (* v v))
20.0ms	(* (/ 1 (* (* 3.0 PI) (- 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
9.0ms	(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1031	1912
1	5001	1634

prune992.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* v v) (* v v))
0.1b	(* 6.0 (* v v))
1.0b	(* (/ 1 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v)))) (+ 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
1.0b	(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-exp-log`
122×	`pow1`
84×	`times-frac`
77×	`add-sqr-sqrt`
68×	`add-cbrt-cube`
55×	`prod-exp`
52×	`*-un-lft-identity`
49×	`add-cube-cbrt`
48×	`div-exp`
36×	`associate-l` `pow-prod-up`
27×	`pow-prod-down` `cbrt-unprod`
26×	`associate-r`
24×	`sqrt-prod`
22×	`pow-sqr`
20×	`cbrt-undiv`
18×	`pow-plus`
13×	`pow2`
11×	`associate-/r/` `unswap-sqr`
8×	`rec-exp` `1-exp`
6×	`associate-/r*` `div-inv`
4×	`sqrt-div` `add-log-exp`
3×	`flip3-+` `-commutative` `flip-+` `associate-/l`
2×	`flip3--` `flip--`
1×	`frac-times` `frac-2neg` `associate-r/` `swap-sqr` `associate-l/` `clear-num`

Counts

4 → 236

Calls

4 calls:

14.0ms	(* (* v v) (* v v))
6.0ms	(* 6.0 (* v v))
85.0ms	(* (/ 1 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v)))) (+ 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
5.0ms	(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (* v v) (* v v))
2.0ms	(* 6.0 (* v v))
22.0ms	(* (/ 1 (/ (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v)))) (+ 1.0 (* v v)))) (/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v))))))
9.0ms	(/ 4.0 (sqrt (- 2.0 (* 6.0 (* v v)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1319	3206
1	5002	2729

prune1.7s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	17
1	29	17

end0.0ms

sample1.4s

Algorithm

intervals

Results

605.0ms	8000×	body	80	valid
598.0ms	8357×	body	80	nan