Details

Time bar (total: 39.0s)

sample249.0ms

Algorithm
intervals
Results
138.0ms109×body1280valid
56.0ms78×body640valid
22.0ms256×pre80true
17.0ms42×body320valid
5.0ms24×body160valid
0.0ms3×body80valid

simplify19.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
18.0ms
(/ (log (- 1 x)) (log (+ 1 x)))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.6b

localize27.0ms

Local error

Found 3 expressions with local error:

6.4b
(log (+ 1 x))
6.3b
(log (- 1 x))
0.0b
(/ (log (- 1 x)) (log (+ 1 x)))

rewrite32.0ms

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
22.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
6.0ms
(log (+ 1 x))
3.0ms
(log (- 1 x))

series161.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
107.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
31.0ms
(log (- 1 x))
23.0ms
(log (+ 1 x))

simplify4.7s

Counts
67 → 82
Calls
67 calls:
Slowest
682.0ms
(- (+ (/ (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)))))))))))
643.0ms
(- (+ (* 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)))))
435.0ms
(/ (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))) (* (* (log (+ 1 x)) (log (+ 1 x))) (log (+ 1 x))))
374.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))
363.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))

prune645.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite50.0ms

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
36.0ms
(+ (- -1 x) (* (* x x) -1/2))
14.0ms
(* (* x x) -1/2)

series85.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
50.0ms
(* (* x x) -1/2)
34.0ms
(+ (- -1 x) (* (* x x) -1/2))

simplify1.5s

Counts
18 → 42
Calls
18 calls:
Slowest
303.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
259.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
225.0ms
(* (exp (- -1 x)) (exp (* (* x x) -1/2)))
205.0ms
(* (/ (exp -1) (exp x)) (exp (* (* x x) -1/2)))
151.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)))

prune290.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

6.4b
(log (+ 1 x))
6.4b
(log (+ x 1))
6.4b
(log (+ (* 1 1) (+ (* x x) (* 1 x))))
1.7b
(log (- 1 (* (* x x) x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
15×log-prod
13×*-un-lft-identity
8×add-sqr-sqrt pow1 log-div add-exp-log add-cube-cbrt
4×add-cbrt-cube rem-log-exp log-pow insert-posit16 add-log-exp
3×flip3-+ flip-+ distribute-lft-out
1×flip3-- flip--
Counts
4 → 63
Calls
4 calls:
Slowest
11.0ms
(log (+ (* 1 1) (+ (* x x) (* 1 x))))
6.0ms
(log (+ 1 x))
3.0ms
(log (+ x 1))
3.0ms
(log (- 1 (* (* x x) x)))

series646.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
543.0ms
(log (- 1 (* (* x x) x)))
45.0ms
(log (+ (* 1 1) (+ (* x x) (* 1 x))))
35.0ms
(log (+ 1 x))
23.0ms
(log (+ x 1))

simplify5.0s

Counts
39 → 75
Calls
39 calls:
Slowest
496.0ms
(- (+ (* 1/3 (pow x 9)) (+ (* 1/2 (pow x 6)) (pow x 3))))
455.0ms
(log (- (pow 1 3) (pow (* (* x x) x) 3)))
406.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
345.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
334.0ms
(- (log -1) (+ (* 3 (log (/ 1 x))) (+ (/ 1 (pow x 3)) (* 1/2 (/ 1 (pow x 6))))))

prune771.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize86.0ms

Local error

Found 4 expressions with local error:

37.0b
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (log (+ x 1)))
6.4b
(log (+ 1 x))
6.4b
(log (+ x 1))
6.4b
(log (+ (* 1 1) (+ (* x x) (* 1 x))))

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
16×add-sqr-sqrt add-cube-cbrt
12×log-prod times-frac
11×pow1
9×add-exp-log
7×log-pow
6×log-div add-cbrt-cube
4×associate-/r* insert-posit16 add-log-exp
3×flip3-+ rem-log-exp flip-+ distribute-lft-out associate-/l*
2×associate-/l/
1×cbrt-undiv clear-num frac-2neg flip3-- div-sub div-exp div-inv flip--
Counts
4 → 83
Calls
4 calls:
Slowest
1.8s
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (log (+ x 1)))
11.0ms
(log (+ (* 1 1) (+ (* x x) (* 1 x))))
4.0ms
(log (+ 1 x))
3.0ms
(log (+ x 1))

series208.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
87.0ms
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (log (+ x 1)))
56.0ms
(log (+ (* 1 1) (+ (* x x) (* 1 x))))
38.0ms
(log (+ x 1))
26.0ms
(log (+ 1 x))

simplify12.3s

Counts
68 → 95
Calls
68 calls:
Slowest
448.0ms
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (sqrt (log (+ x 1))))
443.0ms
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (log (+ x 1)))
400.0ms
(/ (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))) (log (+ x 1)))
365.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
362.0ms
(/ (* (cbrt (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2)))) (cbrt (- (* -1/3 (pow x 9)) (+ (* x (* x x)) (* (* (* (* x x) (* x x)) (* x x)) 1/2))))) (sqrt (log (+ x 1))))

prune1.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes44.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample9.1s

Algorithm
intervals
Results
5.1s3365×body1280valid
2.2s2542×body640valid
776.0ms8000×pre80true
648.0ms1219×body320valid
166.0ms652×body160valid
26.0ms222×body80valid