Details

sample30.0ms

Algorithm

intervals

Results

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

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	27	10
1	72	10
2	194	10
3	416	10
4	816	10
5	1207	10
6	1368	10
7	1505	10
8	1511	10
9	1511	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: 0.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
25×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`times-frac`
20×	`sqrt-prod`
14×	`add-exp-log` `add-cbrt-cube`
12×	`pow1`
7×	`associate-r` `unswap-sqr`
6×	`sqrt-div` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `flip3--` `pow-prod-down` `flip--` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`frac-times` `associate-r/` `-commutative`
1×	`cbrt-undiv` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `associate-*l/` `div-inv`

Counts

4 → 112

Calls

4 calls:

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

series390.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(- 1.0 (* 3.0 (* v v)))
85.0ms	(sqrt (- 1.0 (* 3.0 (* v v))))
219.0ms	(* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
27.0ms	(* 3.0 (* v v))

simplify57.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	521	966
1	1911	911
2	5002	905

prune353.0ms

Filtered

124 candidates to 89 candidates (71.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	2	125

Merged error: 0b

Counts

125 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (cbrt (sqrt 2.0)) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
0.0b	(* (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) 1) (* (/ (cbrt (sqrt 2.0)) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))
0.0b	(sqrt (- 1.0 (* 3.0 (* v v))))
0.2b	(* 3.0 (* v v))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-exp-log`
55×	`add-sqr-sqrt`
52×	`prod-exp`
51×	`frac-times` `add-cbrt-cube`
35×	`associate-l`
33×	`times-frac` `cbrt-unprod`
31×	`associate-*r/`
30×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
27×	`flip3--` `flip--`
22×	`cbrt-prod`
21×	`pow1` `associate-*l/` `sqrt-prod`
18×	`div-exp`
11×	`associate-r`
10×	`cbrt-undiv` `pow-prod-down`
9×	`unswap-sqr`
6×	`1-exp` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`sub-neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `difference-of-squares`

Counts

4 → 192

Calls

4 calls:

15.0ms	(* (/ (cbrt (sqrt 2.0)) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
25.0ms	(* (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) 1) (* (/ (cbrt (sqrt 2.0)) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))
3.0ms	(sqrt (- 1.0 (* 3.0 (* v v))))
6.0ms	(* 3.0 (* v v))

series815.0ms

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (/ (cbrt (sqrt 2.0)) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))
335.0ms	(* (* (/ (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) 1) (* (/ (cbrt (sqrt 2.0)) 4.0) (sqrt (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))
85.0ms	(sqrt (- 1.0 (* 3.0 (* v v))))
32.0ms	(* 3.0 (* v v))

simplify61.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1448	3477
1	5001	2974

prune688.0ms

Filtered

204 candidates to 138 candidates (67.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	203	1	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	205	1	206

Merged error: 0b

Counts

206 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- 1.0 (* 3.0 (* v v))))
0.0b	(* (sqrt (sqrt (- 1.0 (* 3.0 (* v v))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v))))))
0.2b	(* 3.0 (* v v))
0.2b	(* 3.0 (* v v))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

69×	`sqrt-prod`
52×	`add-sqr-sqrt`
38×	`pow1`
33×	`sqrt-pow1`
26×	`sqrt-div`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`pow1/2`
16×	`add-exp-log` `add-cbrt-cube`
15×	`swap-sqr` `associate-l`
11×	`associate-r` `pow-prod-down` `unswap-sqr`
9×	`pow-prod-up`
7×	`flip3--` `prod-exp` `flip--` `cbrt-unprod`
5×	`pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-r/` `associate-l/`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `rem-square-sqrt`

Counts

4 → 144

Calls

4 calls:

3.0ms	(sqrt (- 1.0 (* 3.0 (* v v))))
15.0ms	(* (sqrt (sqrt (- 1.0 (* 3.0 (* v v))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v))))))
6.0ms	(* 3.0 (* v v))
7.0ms	(* 3.0 (* v v))

series235.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (- 1.0 (* 3.0 (* v v))))
88.0ms	(* (sqrt (sqrt (- 1.0 (* 3.0 (* v v))))) (sqrt (sqrt (- 1.0 (* 3.0 (* v v))))))
26.0ms	(* 3.0 (* v v))
33.0ms	(* 3.0 (* v v))

simplify58.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	350	1046
1	1450	969
2	5001	951

prune459.0ms

Filtered

156 candidates to 81 candidates (51.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	156	1	157

Merged error: 0b

Counts

157 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	24
1	27	24

end0.0ms

sample736.0ms

Algorithm

intervals

Results

281.0ms	8000×	body	80	valid
270.0ms	8022×	body	80	nan