Details

sample47.0ms

Algorithm

intervals

Results

18.0ms	256×	body	80	valid
17.0ms	274×	body	80	nan

simplify58.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 2.0 (* 6.0 (* 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))))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
19×	`pow1`
16×	`associate-*r/`
15×	`prod-exp` `cbrt-unprod`
14×	`sqrt-div`
13×	`flip3--` `flip--`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow-prod-down`
8×	`frac-times` `associate-/r/`
7×	`associate-r`
6×	`sqrt-prod`
4×	`cbrt-undiv` `div-exp` `associate-l` `associate-*l/` `add-log-exp`
3×	`times-frac` `associate-/l*`
2×	`*-commutative`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r*` `div-inv` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

2.0ms	(sqrt (- 2.0 (* 6.0 (* v v))))
31.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms	(* 6.0 (* v v))
32.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series807.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(sqrt (- 2.0 (* 6.0 (* v v))))
274.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
28.0ms	(* 6.0 (* v v))
425.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	873	1328
1	4124	1178
2	5002	1175

prune276.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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 (exp (log (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))))
1.0b	(exp (log (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

rewrite276.0ms

Algorithm

rewrite-expression-head

Rules

28×	`pow1`
24×	`associate-*r/`
20×	`add-cbrt-cube`
19×	`add-exp-log`
18×	`add-sqr-sqrt` `flip3--` `sqrt-div` `flip--`
17×	`add-cube-cbrt` `*-un-lft-identity`
16×	`log-div` `exp-diff`
15×	`pow-prod-down`
12×	`frac-times` `times-frac`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-/r/`
7×	`exp-prod` `associate-r`
6×	`associate-*l/`
5×	`log-prod` `exp-sum`
4×	`associate-l` `associate-/r*` `log-pow` `add-log-exp`
3×	`sqrt-prod` `associate-/l*`
2×	`*-commutative`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `rem-exp-log` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

33.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
7.0ms	(* 6.0 (* v v))
127.0ms	(/ 4.0 (exp (log (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))))
104.0ms	(exp (log (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

298.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
25.0ms	(* 6.0 (* v v))
454.0ms	(/ 4.0 (exp (log (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))))
298.0ms	(exp (log (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	862	1832
1	3973	1632
2	5003	1628

prune402.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

121×	`pow1`
75×	`times-frac`
41×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
36×	`add-exp-log` `pow-prod-up`
35×	`add-cbrt-cube`
30×	`sqrt-prod`
26×	`pow-prod-down`
22×	`pow-sqr`
18×	`pow-plus`
16×	`associate-/r/`
14×	`associate-*r/` `prod-exp` `cbrt-unprod`
13×	`pow2`
9×	`associate-/l*`
8×	`flip3--` `flip--` `div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*`
4×	`associate-l` `add-log-exp`
3×	`log-prod`
2×	`log-div` `sqrt-div` `associate-r` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `swap-sqr` `rem-log-exp` `clear-num` `log-pow` `flip-+` `associate-/l/`

Counts

4 → 186

Calls

4 calls:

19.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
12.0ms	(* (* v v) (* v v))
6.0ms	(* 6.0 (* v v))
2.0ms	(log (+ 1.0 (* v v)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

387.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- (* 1.0 1.0) (* (* v v) (* v v))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
39.0ms	(* (* v v) (* v v))
27.0ms	(* 6.0 (* v v))
110.0ms	(log (+ 1.0 (* v v)))

simplify125.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	963	2400
1	4283	2209
2	5001	2184

prune503.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

565.0ms	8000×	body	80	valid
528.0ms	8188×	body	80	nan