Details

Time bar (total: 27.0s)

sample222.0ms

Algorithm
intervals
Results
117.0ms97×body1280valid
63.0ms84×body640valid
17.0ms49×body320valid
9.0ms256×pre80true
3.0ms16×body160valid
1.0ms10×body80valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(/ (log (- 1 x)) (log (+ 1 x)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.3b

localize14.0ms

Local error

Found 3 expressions with local error:

5.0b
(log (+ 1 x))
5.0b
(log (- 1 x))
0.0b
(/ (log (- 1 x)) (log (+ 1 x)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
18×add-sqr-sqrt
16×times-frac
15×pow1 add-cube-cbrt
12×log-pow
10×log-prod
7×add-exp-log
6×log-div
5×add-cbrt-cube
4×associate-/r* associate-/l*
3×insert-posit16 add-log-exp
2×flip3-- div-sub rem-log-exp flip-- difference-of-squares
1×cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ div-inv distribute-lft-out distribute-lft-out--
Counts
3 → 73
Calls
3 calls:
Slowest
26.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
3.0ms
(log (- 1 x))
3.0ms
(log (+ 1 x))

series193.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
118.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
39.0ms
(log (- 1 x))
36.0ms
(log (+ 1 x))

simplify4.9s

Counts
67 → 82
Calls
67 calls:
Slowest
830.0ms
(- (+ (/ (log (/ -1 x)) (* x (pow (- (log -1) (log (/ -1 x))) 2))) (/ 1 (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (+ (/ (log (/ -1 x)) (- (log -1) (log (/ -1 x)))) (+ (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 3))) (+ (/ 1 (* x (- (log -1) (log (/ -1 x))))) (+ (* 1/2 (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (* 1/2 (/ 1 (* (pow x 2) (- (log -1) (log (/ -1 x)))))))))))
479.0ms
(/ (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))) (* (* (log (+ 1 x)) (log (+ 1 x))) (log (+ 1 x))))
418.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
376.0ms
(- (+ (* 2 (/ 1 (* (pow (log (/ 1 x)) 2) (pow x 2)))) (+ (* 2 (/ 1 (* (log (/ 1 x)) x))) (+ (* 1/2 (/ (log -1) (* (pow (log (/ 1 x)) 2) (pow x 2)))) 1))) (+ (/ (log -1) (* (pow (log (/ 1 x)) 3) (pow x 2))) (+ (/ (log -1) (log (/ 1 x))) (/ (log -1) (* (pow (log (/ 1 x)) 2) x)))))
372.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))

prune742.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (- -1 x) (* (* x x) -1/2))
0.0b
(* (* x x) -1/2)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-cbrt-cube add-exp-log add-log-exp
4×add-sqr-sqrt
3×*-un-lft-identity associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×associate-+l+ sum-log insert-posit16
1×+-commutative sub-neg flip3-+ diff-log associate-*l* *-commutative associate-+l- flip-+ unswap-sqr
Counts
2 → 36
Calls
2 calls:
Slowest
42.0ms
(+ (- -1 x) (* (* x x) -1/2))
23.0ms
(* (* x x) -1/2)

series64.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
37.0ms
(* (* x x) -1/2)
27.0ms
(+ (- -1 x) (* (* x x) -1/2))

simplify1.3s

Counts
18 → 42
Calls
18 calls:
Slowest
235.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
218.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
188.0ms
(* (exp (- -1 x)) (exp (* (* x x) -1/2)))
180.0ms
(* (/ (exp -1) (exp x)) (exp (* (* x x) -1/2)))
129.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)))

prune293.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (* x x) -1/2)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-cbrt-cube add-exp-log
3×add-sqr-sqrt associate-*r* pow-prod-down prod-exp cbrt-unprod
2×*-un-lft-identity add-cube-cbrt
1×associate-*l* *-commutative insert-posit16 add-log-exp unswap-sqr
Counts
1 → 20
Calls
1 calls:
Slowest
25.0ms
(* (* x x) -1/2)

series29.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
29.0ms
(* (* x x) -1/2)

simplify695.0ms

Counts
13 → 23
Calls
13 calls:
Slowest
298.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
218.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
29.0ms
(+ (+ (log x) (log x)) (log -1/2))
28.0ms
(+ (log (* x x)) (log -1/2))
21.0ms
(* -1/2 (pow x 2))

prune184.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

5.0b
(log (- 1 x))
5.0b
(log (- 1 x))
2.6b
(log (- 1 (* x x)))
0.0b
(/ (log (- 1 x)) (- (log (- 1 (* x x))) (log (- 1 x))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
38×add-sqr-sqrt
36×pow1
32×times-frac log-pow
22×distribute-lft-out--
21×add-cube-cbrt
17×log-prod
11×difference-of-squares
9×add-exp-log
8×log-div associate-/r*
6×add-cbrt-cube
5×flip3-- flip--
4×insert-posit16 associate-/l* add-log-exp
3×rem-log-exp
2×div-sub associate-/r/
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 114
Calls
4 calls:
Slowest
21.0ms
(/ (log (- 1 x)) (- (log (- 1 (* x x))) (log (- 1 x))))
7.0ms
(log (- 1 x))
3.0ms
(log (- 1 x))
3.0ms
(log (- 1 (* x x)))

series341.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(/ (log (- 1 x)) (- (log (- 1 (* x x))) (log (- 1 x))))
134.0ms
(log (- 1 (* x x)))
32.0ms
(log (- 1 x))
29.0ms
(log (- 1 x))

simplify7.8s

Counts
118 → 126
Calls
118 calls:
Slowest
851.0ms
(- (+ (/ (log (/ -1 x)) (* x (pow (- (log -1) (log (/ -1 x))) 2))) (/ 1 (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (+ (/ (log (/ -1 x)) (- (log -1) (log (/ -1 x)))) (+ (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 3))) (+ (/ 1 (* x (- (log -1) (log (/ -1 x))))) (+ (* 1/2 (/ (log (/ -1 x)) (* (pow x 2) (pow (- (log -1) (log (/ -1 x))) 2)))) (* 1/2 (/ 1 (* (pow x 2) (- (log -1) (log (/ -1 x)))))))))))
526.0ms
(- (+ x (+ (* 1/3 (pow x 3)) (* 1/2 (pow x 2)))))
405.0ms
(- (log -1) (+ (* 2 (log (/ 1 x))) (+ (* 1/2 (/ 1 (pow x 4))) (/ 1 (pow x 2)))))
396.0ms
(- (+ (pow x 2) (+ (* 1/2 (pow x 4)) (* 1/3 (pow x 6)))))
365.0ms
(/ (log (- (pow 1 3) (pow x 3))) (- (log (- 1 (* x x))) (log (- 1 x))))

prune662.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample9.3s

Algorithm
intervals
Results
5.4s3444×body1280valid
2.5s2503×body640valid
593.0ms1244×body320valid
347.0ms8000×pre80true
188.0ms577×body160valid
27.0ms232×body80valid