Details

sample31.0ms

Algorithm

intervals

Results

10.0ms	274×	body	80	nan
9.0ms	256×	body	80	valid

simplify62.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

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))))))

rewrite43.0ms

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)))
12.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
6.0ms	(* 6.0 (* v v))
13.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

series844.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
275.0ms	(* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))
25.0ms	(* 6.0 (* v v))
430.0ms	(/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v))))))

simplify112.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (97.0ms)

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

prune316.0ms

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 173

Calls

4 calls:

7.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
13.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
7.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms	(* 6.0 (* v v))

series680.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (* 3.0 PI) (- 1.0 (* v v)))
438.0ms	(/ (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))) (sqrt (- 2.0 (* 6.0 (* v v)))))
101.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
26.0ms	(* 6.0 (* v v))

simplify118.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1000	2299
1	4704	2105
2	5001	2101

prune453.0ms

Filtered

185 candidates to 129 candidates (69.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	186	1	187

Merged error: 0b

Counts

187 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))))
0.0b	(/ (expm1 (log1p (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
0.0b	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
0.2b	(* 6.0 (* v v))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`times-frac`
20×	`add-exp-log` `add-cbrt-cube`
12×	`sqrt-prod`
9×	`pow1`
7×	`associate-/r*`
6×	`prod-exp` `cbrt-unprod` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `pow-prod-down`
2×	`flip3--` `frac-2neg` `sqrt-div` `associate-*r/` `clear-num` `flip--` `div-inv` `expm1-udef`
1×	`expm1-log1p` `div-sub` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

1.0ms	(expm1 (log1p (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))))
5.0ms	(/ (expm1 (log1p (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
8.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
6.0ms	(* 6.0 (* v v))

series2.0s

Counts

4 → 12

Calls

4 calls:

727.0ms	(expm1 (log1p (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))))
1.1s	(/ (expm1 (log1p (/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v)))))) (sqrt (- 2.0 (* 6.0 (* v v)))))
102.0ms	(/ 4.0 (* (* 3.0 PI) (- 1.0 (* v v))))
26.0ms	(* 6.0 (* v v))

simplify84.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	793	1465
1	3486	1274
2	5002	1260

prune329.0ms

Filtered

115 candidates to 83 candidates (72.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	1	116

Merged error: 0b

Counts

116 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	12
1	21	12

end0.0ms

sample779.0ms

Algorithm

intervals

Results

300.0ms	8000×	body	80	valid
290.0ms	8022×	body	80	nan