Details

Time bar (total: 47.2s)

sample151.0ms

Algorithm
intervals
Results
71.0ms116×body1280valid
27.0ms257×body80nan
22.0ms68×body640valid
9.0ms42×body320valid
2.0ms20×body160valid
1.0ms10×body80valid

simplify111.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 57.9b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ 1.0 x) (- 1.0 x))
5.3b
(log (/ (+ 1.0 x) (- 1.0 x)))

rewrite74.0ms

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:
39.0ms
(/ (+ 1.0 x) (- 1.0 x))
18.0ms
(log (/ (+ 1.0 x) (- 1.0 x)))

series212.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ (+ 1.0 x) (- 1.0 x))
171.0ms
(log (/ (+ 1.0 x) (- 1.0 x)))

simplify1.5s

Counts
88 → 88

prune339.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite88.0ms

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:
73.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

series70.0ms

Counts
1 → 3
Calls
1 calls:
70.0ms
(* 2.0 (/ (pow x 2) (pow 1.0 2)))

simplify953.0ms

Counts
113 → 113

prune472.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log (sqrt (+ 1.0 x))) (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))
0.0b
(/ (sqrt (+ 1.0 x)) (- 1.0 x))
5.3b
(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))
5.4b
(log (sqrt (+ 1.0 x)))

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
148×*-un-lft-identity
108×add-sqr-sqrt
105×times-frac
96×log-prod
72×sqrt-prod
64×add-cube-cbrt
41×associate-+r+
22×distribute-lft-out distribute-lft-out-- difference-of-squares
11×pow1
10×add-exp-log
8×log-pow
7×associate-+l+ associate-/l*
6×log-div sqrt-div associate-/r/ add-cbrt-cube
5×associate-/r*
4×flip3-+ flip-+ add-log-exp
3×flip3-- rem-log-exp flip-- div-inv
2×associate-+l- div-exp associate-/l/
1×cbrt-undiv +-commutative associate-+r- frac-2neg sqrt-pow1 pow1/2 clear-num sum-log
Counts
4 → 201
Calls
4 calls:
33.0ms
(+ (log (sqrt (+ 1.0 x))) (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))
40.0ms
(/ (sqrt (+ 1.0 x)) (- 1.0 x))
30.0ms
(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))
12.0ms
(log (sqrt (+ 1.0 x)))

series920.0ms

Counts
4 → 12
Calls
4 calls:
441.0ms
(+ (log (sqrt (+ 1.0 x))) (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))
111.0ms
(/ (sqrt (+ 1.0 x)) (- 1.0 x))
242.0ms
(log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))
126.0ms
(log (sqrt (+ 1.0 x)))

simplify1.1s

Counts
213 → 213

prune723.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2)))))
0.0b
(- (- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2))))) (+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))))
0.1b
(+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4))))
0.1b
(* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))

rewrite27.7s

Algorithm
rewrite-expression-head
Rules
96×times-frac
90×add-sqr-sqrt unpow-prod-down add-log-exp
84×associate-*r*
62×associate-*r/
52×*-un-lft-identity
50×add-cube-cbrt
44×frac-sub
42×sum-log
40×frac-add
31×diff-log
28×sqrt-prod
27×add-exp-log
26×sqr-pow
18×flip3-+ flip-+
17×unswap-sqr
14×unpow2
10×prod-exp
9×flip3-- div-exp add-cbrt-cube flip--
6×pow1 pow-to-exp pow-exp
5×frac-times associate-*l/ associate--l+
3×sub-neg associate-*l*
2×cbrt-unprod
1×cbrt-undiv +-commutative associate--l- associate-+l+ pow-prod-down *-commutative div-inv associate--r+ distribute-lft-out-- difference-of-squares
Counts
4 → 223
Calls
4 calls:
4.9s
(- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2)))))
22.5s
(- (- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2))))) (+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))))
205.0ms
(+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4))))
87.0ms
(* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))

series1.5s

Counts
4 → 12
Calls
4 calls:
435.0ms
(- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2)))))
579.0ms
(- (- (+ (+ (* 1.0 (+ (/ x (pow (sqrt 1.0) 2)) x)) (+ (log (sqrt 1.0)) (log (* 1.0 (sqrt 1.0))))) (* 1.0 (pow x 2))) (* 0.125 (/ (pow x 2) (* (pow (sqrt 1.0) 4) (pow 1.0 2))))) (+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))))
311.0ms
(+ (+ (* (/ 0.5 1.0) (/ (pow x 2) (pow 1.0 2))) (* 0.5 (/ (pow x 2) (pow 1.0 2)))) (* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4))))
152.0ms
(* 0.375 (/ (pow x 2) (pow (sqrt 1.0) 4)))

simplify1.1s

Counts
235 → 235

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

regimes131.0ms

Accuracy

0% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 0.8b

bsearch0.0ms

simplify1.5s

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.6s3371×body1280valid
1.3s2457×body640valid
958.0ms8084×body80nan
420.0ms1271×body320valid
105.0ms650×body160valid
19.0ms251×body80valid