Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
6.0ms	229×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	7
1	39	7
2	61	7
3	80	7
4	105	7
5	114	7
6	114	7

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.1b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

217×	`*-un-lft-identity`
98×	`times-frac`
96×	`distribute-lft-out`
73×	`add-sqr-sqrt`
56×	`associate-l`
41×	`add-cube-cbrt`
40×	`associate-r`
14×	`associate-/l*`
8×	`*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`sum-log`
2×	`pow1` `cbrt-undiv` `+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `div-exp` `associate-/r/` `flip-+` `associate-/l/`
1×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv`

Counts

2 → 155

Calls

2 calls:

11.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
23.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series137.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
91.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify80.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	504	1684
1	2139	1620
2	5001	1619

prune176.0ms

Filtered

161 candidates to 75 candidates (53.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	158	3	161
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	3	162

Merged error: 0b

Counts

162 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) 6.0)
0.0b	(/ (- x 1.0) (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) 6.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

401×	`*-un-lft-identity`
272×	`times-frac`
161×	`add-sqr-sqrt`
144×	`distribute-lft-out`
109×	`add-cube-cbrt`
48×	`associate-l`
31×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
19×	`associate-/l*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `add-log-exp`
6×	`associate-/l/`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+`
2×	`+-commutative` `associate-+l+`
1×	`flip3--` `div-sub` `flip--`

Counts

3 → 250

Calls

3 calls:

10.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
14.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) 6.0)
22.0ms	(/ (- x 1.0) (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) 6.0))

series193.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
50.0ms	(/ (+ (+ x 1.0) (* 4.0 (sqrt x))) 6.0)
97.0ms	(/ (- x 1.0) (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) 6.0))

simplify110.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	735	2912
1	2877	2815
2	5001	2815

prune293.0ms

Filtered

259 candidates to 125 candidates (51.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	258	1	259
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	260	2	262

Merged error: 0b

Counts

262 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.0b	(/ (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) (/ 1 6.0))
0.1b	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

1491×	`*-un-lft-identity`
1436×	`times-frac`
711×	`add-sqr-sqrt`
497×	`add-cube-cbrt`
468×	`distribute-lft-out`
156×	`associate-l`
107×	`distribute-lft-out--` `difference-of-squares`
58×	`div-inv`
54×	`associate-/l*`
39×	`associate-/r/`
30×	`associate-/r*`
27×	`add-exp-log`
21×	`associate-/l/`
17×	`div-exp` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
9×	`cbrt-undiv`
8×	`add-log-exp`
4×	`frac-2neg` `clear-num`
3×	`pow1` `div-sub` `sum-log`
2×	`+-commutative` `rec-exp` `associate-+l+` `flip3--` `1-exp` `flip--`

Counts

3 → 718

Calls

3 calls:

10.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
37.0ms	(/ (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) (/ 1 6.0))
15.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series228.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
92.0ms	(/ (/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x)))) (/ 1 6.0))
88.0ms	(/ (- x 1.0) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify166.0ms

Algorithm

egg-herbie

Counts

727 → 727

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	1937	11605
1	5001	10882

prune829.0ms

Filtered

727 candidates to 239 candidates (67.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	727	0	727
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	727	2	729

Merged error: 0b

Counts

729 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
5.8b	(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
8.0b	(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
15.6b	(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

rewrite659.0ms

Algorithm

rewrite-expression-head

Rules

1274×	`*-un-lft-identity`
822×	`frac-times`
562×	`associate-l`
528×	`frac-add`
445×	`add-sqr-sqrt`
434×	`distribute-lft-out`
431×	`flip3-+` `flip-+`
384×	`unpow-prod-down`
338×	`times-frac`
297×	`associate-r`
284×	`flip3--` `flip--`
280×	`associate-/l*`
240×	`associate-/r*`
202×	`add-cube-cbrt`
192×	`pow-unpow` `sum-cubes`
190×	`associate-*r/`
163×	`associate-*l/`
98×	`distribute-lft-out--`
81×	`unswap-sqr`
50×	`*-commutative`
45×	`pow1`
44×	`difference-of-squares`
40×	`associate-/l/`
30×	`add-exp-log` `add-cbrt-cube`
26×	`sqrt-prod`
22×	`swap-sqr`
20×	`frac-2neg` `clear-num`
18×	`pow-prod-down`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`prod-exp` `cbrt-unprod`
12×	`associate-+l+`
9×	`+-commutative` `add-log-exp`
6×	`associate-+r+`
4×	`cbrt-undiv` `div-exp` `associate-/r/` `pow-sqr` `pow-prod-up`
3×	`sub-neg`
2×	`pow-plus` `sum-log` `div-inv`
1×	`pow2` `associate-+r-` `diff-log`

Counts

4 → 1219

Calls

4 calls:

17.0ms	(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
30.0ms	(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
177.0ms	(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
297.0ms	(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* 4.0 (sqrt x)) (* 4.0 (sqrt x)))
97.0ms	(/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3)))
83.0ms	(+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x)))))
208.0ms	(* (/ (* 6.0 (- x 1.0)) (+ (pow (+ x 1.0) 3) (pow (* 4.0 (sqrt x)) 3))) (+ (* (+ x 1.0) (+ x 1.0)) (- (* (* 4.0 (sqrt x)) (* 4.0 (sqrt x))) (* (+ x 1.0) (* 4.0 (sqrt x))))))

simplify575.0ms

Algorithm

egg-herbie

Counts

1231 → 1231

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5003	63706

prune3.6s

Filtered

1231 candidates to 658 candidates (46.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	1231	0	1231
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	1231	2	1233

Merged error: 0b

Counts

1233 → 2

regimes14.0ms

Accuracy

0% (0.0b 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	18	8
1	18	8

end0.0ms

sample635.0ms

Algorithm

intervals

Results

245.0ms	8000×	body	80	valid
208.0ms	7872×	body	80	nan