Details

sample25.0ms

Algorithm

intervals

Results

6.0ms	319×	body	80	nan
6.0ms	284×	body	80	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	4
1	23	4
2	40	4
3	59	4
4	74	4
5	103	4
6	120	4
7	145	4
8	226	4
9	257	4
10	257	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (- 1.0 x) (* y (sqrt x)))
0.3b	(* y (sqrt x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`associate-r`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`associate-l`
2×	`associate-+l+` `sum-log` `unswap-sqr`
1×	`+-commutative` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

2 → 37

Calls

2 calls:

13.0ms	(+ (- 1.0 x) (* y (sqrt x)))
4.0ms	(* y (sqrt x))

series84.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(+ (- 1.0 x) (* y (sqrt x)))
47.0ms	(* y (sqrt x))

simplify143.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	240	231
1	957	202
2	4716	192
3	5001	192

prune94.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt x))
0.1b	(sqrt (sqrt x))
0.2b	(* y (sqrt (sqrt x)))
0.4b	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
25×	`add-sqr-sqrt`
18×	`associate-r`
15×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
8×	`sqrt-pow1`
4×	`rem-sqrt-square` `pow1/2` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`unswap-sqr`
2×	`*-commutative`

Counts

4 → 88

Calls

4 calls:

1.0ms	(sqrt (sqrt x))
1.0ms	(sqrt (sqrt x))
6.0ms	(* y (sqrt (sqrt x)))
16.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(sqrt (sqrt x))
143.0ms	(sqrt (sqrt x))
83.0ms	(* y (sqrt (sqrt x)))
41.0ms	(* (* y (sqrt (sqrt x))) (sqrt (sqrt x)))

simplify49.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	336	516
1	1481	454
2	5001	427

prune205.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (/ 1 x) -1/4)
0.1b	(sqrt (sqrt x))
0.2b	(* y (pow (/ 1 x) -1/4))
0.4b	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
38×	`add-sqr-sqrt`
29×	`unpow-prod-down`
27×	`*-un-lft-identity`
26×	`add-cube-cbrt` `associate-r`
20×	`times-frac`
19×	`prod-exp` `sqrt-prod`
12×	`pow-exp`
11×	`add-cbrt-cube`
10×	`pow1`
6×	`div-exp`
5×	`unswap-sqr`
4×	`sqrt-pow1` `associate-l` `cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `pow-pow` `1-exp` `sqr-pow`
2×	`rem-sqrt-square` `pow1/2` `*-commutative` `div-inv`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 119

Calls

4 calls:

3.0ms	(pow (/ 1 x) -1/4)
1.0ms	(sqrt (sqrt x))
14.0ms	(* y (pow (/ 1 x) -1/4))
20.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(pow (/ 1 x) -1/4)
138.0ms	(sqrt (sqrt x))
66.0ms	(* y (pow (/ 1 x) -1/4))
83.0ms	(* (* y (pow (/ 1 x) -1/4)) (sqrt (sqrt x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	573	745
1	2586	663
2	5001	661

prune312.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 x))
0.2b	(* y (* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4)))
0.4b	(* (* y (* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4))) (sqrt (sqrt x)))
0.5b	(* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
120×	`unpow-prod-down`
116×	`sqrt-prod`
74×	`add-exp-log`
71×	`times-frac`
66×	`*-un-lft-identity`
58×	`prod-exp`
51×	`add-cube-cbrt`
37×	`unswap-sqr`
30×	`associate-r`
24×	`swap-sqr` `associate-l`
20×	`add-cbrt-cube`
18×	`pow-to-exp` `pow-exp`
16×	`sqr-pow`
13×	`pow1`
10×	`cbrt-unprod`
7×	`div-inv`
5×	`pow-prod-down`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `*-commutative`
1×	`pow2` `pow-flip` `pow1/2` `sqrt-div` `pow-sqr` `pow-prod-up` `inv-pow`

Counts

4 → 210

Calls

4 calls:

2.0ms	(sqrt (/ 1 x))
32.0ms	(* y (* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4)))
116.0ms	(* (* y (* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4))) (sqrt (sqrt x)))
42.0ms	(* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4))

series306.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (/ 1 x))
74.0ms	(* y (* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4)))
75.0ms	(* (* y (* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4))) (sqrt (sqrt x)))
134.0ms	(* (pow (sqrt (/ 1 x)) -1/4) (pow (sqrt (/ 1 x)) -1/4))

simplify88.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	636	2146
1	2900	1733
2	5002	1658

prune471.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes96.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	4
1	9	4

end0.0ms

sample785.0ms

Algorithm

intervals

Results

328.0ms	8542×	body	80	valid
178.0ms	8715×	body	80	nan
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	320	valid