Details

Time bar (total: 10.7s)

sample160.0ms

Algorithm
intervals
Results
87.0ms122×body1280valid
28.0ms74×body640valid
13.0ms238×body80nan
9.0ms39×body320valid
2.0ms17×body160valid
0.0ms4×body80valid

simplify6.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.8b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ 1.0 x) (- 1.0 x))
4.7b
(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
41×add-sqr-sqrt
40×times-frac
26×log-prod
23×add-cube-cbrt
11×distribute-lft-out
9×distribute-lft-out-- difference-of-squares
7×add-exp-log
5×associate-/r*
4×associate-/r/ add-cbrt-cube associate-/l*
3×pow1
2×flip3-- div-exp rem-log-exp flip-- div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 82
Calls
2 calls:
43.0ms
(/ (+ 1.0 x) (- 1.0 x))
12.0ms
(log (/ (+ 1.0 x) (- 1.0 x)))

series228.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(/ (+ 1.0 x) (- 1.0 x))
180.0ms
(log (/ (+ 1.0 x) (- 1.0 x)))

simplify71.0ms

Counts
88 → 88

prune227.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
69×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
35×add-cube-cbrt *-un-lft-identity
24×add-exp-log unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 110
Calls
1 calls:
58.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

simplify40.0ms

Counts
113 → 113

prune400.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3)))
0.0b
(* (/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
4.7b
(log (* (/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
286×add-sqr-sqrt
257×*-un-lft-identity
201×times-frac
144×difference-of-squares
108×unpow-prod-down cube-prod
106×associate-*l*
72×sqr-pow
65×add-cube-cbrt
51×distribute-lft-out
45×distribute-lft-out--
25×associate-/r*
16×add-exp-log
10×add-cbrt-cube
9×difference-cubes
8×pow1
5×log-div flip3-+ flip-+
4×frac-times associate-*r/ prod-exp associate-/r/ associate-/l*
3×div-exp rem-log-exp associate-*r* add-log-exp
2×cbrt-undiv flip3-- pow-prod-down associate-*l/ log-pow flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
1×distribute-rgt-in log-prod frac-2neg distribute-lft-in clear-num *-commutative
Counts
3 → 294
Calls
3 calls:
61.0ms
(/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3)))
208.0ms
(* (/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
79.0ms
(log (* (/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

series348.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3)))
75.0ms
(* (/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
219.0ms
(log (* (/ (+ 1.0 x) (- (pow 1.0 3) (pow x 3))) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

simplify57.0ms

Counts
303 → 303

prune881.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (log (* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))) (log (- (pow 1.0 3) (pow x 3))))
0.0b
(* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
1.8b
(log (- (pow 1.0 3) (pow x 3)))
4.7b
(log (* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

rewrite519.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
52×log-prod
35×*-un-lft-identity
33×difference-of-squares
25×associate--r+
24×unpow-prod-down cube-prod
20×log-div
19×pow1
18×flip3-+ flip-+
16×distribute-lft-out-- sqr-pow
12×frac-times
10×add-exp-log log-pow
8×associate--l- add-cube-cbrt
6×associate-*r/ associate-*l/ add-cbrt-cube
4×associate-*l* pow-prod-down add-log-exp
3×flip3-- rem-log-exp associate-*r* flip--
2×difference-cubes prod-exp associate--r-
1×distribute-rgt-in sub-neg distribute-lft-in diff-log associate--l+ *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 140
Calls
4 calls:
318.0ms
(- (log (* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))) (log (- (pow 1.0 3) (pow x 3))))
123.0ms
(* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
38.0ms
(log (- (pow 1.0 3) (pow x 3)))
33.0ms
(log (* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

series851.0ms

Counts
4 → 12
Calls
4 calls:
340.0ms
(- (log (* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))) (log (- (pow 1.0 3) (pow x 3))))
60.0ms
(* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x))))
314.0ms
(log (- (pow 1.0 3) (pow x 3)))
137.0ms
(log (* (+ 1.0 x) (+ (* 1.0 1.0) (+ (* x x) (* 1.0 x)))))

simplify112.0ms

Counts
152 → 152

prune726.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

regimes18.0ms

Accuracy

0.1% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify52.0ms

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.8s3398×body1280valid
999.0ms2561×body640valid
742.0ms8071×body80nan
295.0ms1229×body320valid
88.0ms612×body160valid
14.0ms200×body80valid