Details

Time bar (total: 27.0s)

sample270.0ms

Algorithm
intervals
Results
143.0ms95×body1280valid
79.0ms91×body640valid
19.0ms41×body320valid
10.0ms256×pre80true
7.0ms23×body160valid
1.0ms6×body80valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(/ (log (- 1 x)) (log (+ 1 x)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.3b

localize27.0ms

Local error

Found 3 expressions with local error:

8.3b
(log (- 1 x))
8.1b
(log (+ 1 x))
0.0b
(/ (log (- 1 x)) (log (+ 1 x)))

rewrite54.0ms

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
40.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
7.0ms
(log (- 1 x))
6.0ms
(log (+ 1 x))

series163.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
84.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
41.0ms
(log (- 1 x))
38.0ms
(log (+ 1 x))

simplify4.5s

Counts
67 → 82
Calls
67 calls:
Slowest
843.0ms
(- (+ (/ (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)))))))))))
426.0ms
(/ (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))) (* (* (log (+ 1 x)) (log (+ 1 x))) (log (+ 1 x))))
359.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
353.0ms
(- (+ (* 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)))))
326.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))

prune733.0ms

Pruning

5 alts after pruning (5 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)

rewrite45.0ms

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
23.0ms
(+ (- -1 x) (* (* x x) -1/2))
21.0ms
(* (* x x) -1/2)

series82.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
48.0ms
(* (* x x) -1/2)
34.0ms
(+ (- -1 x) (* (* x x) -1/2))

simplify1.5s

Counts
18 → 42
Calls
18 calls:
Slowest
280.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
254.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
245.0ms
(* (exp (- -1 x)) (exp (* (* x x) -1/2)))
180.0ms
(* (/ (exp -1) (exp x)) (exp (* (* x x) -1/2)))
149.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)))

prune259.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

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
13.0ms
(* (* x x) -1/2)

series27.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
27.0ms
(* (* x x) -1/2)

simplify676.0ms

Counts
13 → 23
Calls
13 calls:
Slowest
266.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
238.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
29.0ms
(+ (log (* x x)) (log -1/2))
26.0ms
(+ (+ (log x) (log x)) (log -1/2))
20.0ms
(* -1/2 (pow x 2))

prune169.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

8.1b
(log (+ 1 x))
8.1b
(log (+ 1 x))
3.4b
(log (- 1 (* x x)))
0.0b
(/ (- (log (- 1 (* x x))) (log (+ 1 x))) (log (+ 1 x)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
36×pow1
32×add-sqr-sqrt times-frac log-pow
21×add-cube-cbrt
20×distribute-lft-out--
13×log-prod
9×add-exp-log
8×associate-/l*
7×difference-of-squares
6×log-div add-cbrt-cube
4×associate-/r* insert-posit16 add-log-exp
3×rem-log-exp
2×flip3-+ flip3-- flip-+ flip-- distribute-lft-out associate-/l/
1×cbrt-undiv clear-num frac-2neg div-sub div-exp div-inv
Counts
4 → 109
Calls
4 calls:
Slowest
19.0ms
(/ (- (log (- 1 (* x x))) (log (+ 1 x))) (log (+ 1 x)))
3.0ms
(log (+ 1 x))
3.0ms
(log (- 1 (* x x)))
3.0ms
(log (+ 1 x))

series343.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(/ (- (log (- 1 (* x x))) (log (+ 1 x))) (log (+ 1 x)))
139.0ms
(log (- 1 (* x x)))
38.0ms
(log (+ 1 x))
26.0ms
(log (+ 1 x))

simplify7.9s

Counts
110 → 121
Calls
110 calls:
Slowest
771.0ms
(- (+ (/ (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)))))))))))
398.0ms
(- (log -1) (+ (* 2 (log (/ 1 x))) (+ (* 1/2 (/ 1 (pow x 4))) (/ 1 (pow x 2)))))
395.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
381.0ms
(- (log -1) (+ (* 2 (log (/ -1 x))) (+ (* 1/2 (/ 1 (pow x 4))) (/ 1 (pow x 2)))))
378.0ms
(- (+ (pow x 2) (+ (* 1/2 (pow x 4)) (* 1/3 (pow x 6)))))

prune714.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
6.0s3473×body1280valid
2.1s2481×body640valid
716.0ms1189×body320valid
334.0ms8000×pre80true
178.0ms643×body160valid
27.0ms214×body80valid