Details

Time bar (total: 34.5s)

sample249.0ms

Algorithm
intervals
Results
148.0ms120×body1280valid
57.0ms77×body640valid
16.0ms39×body320valid
9.0ms256×pre80true
3.0ms16×body160valid
1.0ms4×body80valid

simplify12.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.8b

localize13.0ms

Local error

Found 3 expressions with local error:

5.2b
(log (+ 1 x))
5.2b
(log (- 1 x))
0.0b
(/ (log (- 1 x)) (log (+ 1 x)))

rewrite58.0ms

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
28.0ms
(log (- 1 x))
25.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
3.0ms
(log (+ 1 x))

series178.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
124.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
27.0ms
(log (+ 1 x))
27.0ms
(log (- 1 x))

simplify6.2s

Counts
113 → 82
Calls
113 calls:
Slowest
770.0ms
(- (+ (/ (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)))))))))))
519.0ms
(/ (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))) (* (* (log (+ 1 x)) (log (+ 1 x))) (log (+ 1 x))))
418.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))
393.0ms
(- (+ (* 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)))))
378.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))

prune721.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite52.0ms

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
37.0ms
(+ (- -1 x) (* (* x x) -1/2))
14.0ms
(* (* x x) -1/2)

series77.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
50.0ms
(* (* x x) -1/2)
27.0ms
(+ (- -1 x) (* (* x x) -1/2))

simplify4.1s

Counts
43 → 42
Calls
43 calls:
Slowest
392.0ms
(+ (pow (- -1 x) 3) (pow (* (* x x) -1/2) 3))
383.0ms
(+ (* (- -1 x) (- -1 x)) (- (* (* (* x x) -1/2) (* (* x x) -1/2)) (* (- -1 x) (* (* x x) -1/2))))
259.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
256.0ms
(- (* (- -1 x) (- -1 x)) (* (* (* x x) -1/2) (* (* x x) -1/2)))
254.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))

prune321.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite28.0ms

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
28.0ms
(* (* x x) -1/2)

series38.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
38.0ms
(* (* x x) -1/2)

simplify1.3s

Counts
23 → 23
Calls
23 calls:
Slowest
324.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
308.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
270.0ms
(* (* (* (* x x) -1/2) (* (* x x) -1/2)) (* (* x x) -1/2))
59.0ms
(exp (* (* x x) -1/2))
31.0ms
(+ (log (* x x)) (log -1/2))

prune202.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

5.3b
(log (sqrt (+ 1 x)))
5.3b
(log (sqrt (+ 1 x)))
5.2b
(log (- 1 x))
0.0b
(/ (log (- 1 x)) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x)))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
143×log-pow
115×pow1
100×times-frac
97×*-un-lft-identity
63×add-sqr-sqrt
60×add-cube-cbrt
50×distribute-rgt-out
42×distribute-lft-out
32×sqrt-pow1 pow1/2
25×associate-/r*
20×log-prod
10×distribute-lft1-in distribute-rgt1-in
9×add-exp-log
8×log-div sqrt-prod
6×add-cbrt-cube
4×sqrt-div insert-posit16 associate-/l* add-log-exp
3×flip3-+ rem-log-exp flip-+
2×flip3-- div-sub associate-/r/ flip-- difference-of-squares
1×cbrt-undiv clear-num frac-2neg div-exp div-inv distribute-lft-out--
Counts
4 → 206
Calls
4 calls:
Slowest
24.0ms
(/ (log (- 1 x)) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x)))))
4.0ms
(log (- 1 x))
4.0ms
(log (sqrt (+ 1 x)))
3.0ms
(log (sqrt (+ 1 x)))

series473.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(/ (log (- 1 x)) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x)))))
97.0ms
(log (sqrt (+ 1 x)))
81.0ms
(log (sqrt (+ 1 x)))
41.0ms
(log (- 1 x))

simplify9.5s

Counts
344 → 218
Calls
344 calls:
Slowest
360.0ms
(/ (log (- 1 x)) (+ (pow (log (sqrt (+ 1 x))) 3) (pow (log (sqrt (+ 1 x))) 3)))
352.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))
334.0ms
(/ (log (- (pow 1 3) (pow x 3))) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x)))))
317.0ms
(* (* (/ (log (- 1 x)) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x))))) (/ (log (- 1 x)) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x)))))) (/ (log (- 1 x)) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x))))))
301.0ms
(/ (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))) (* (* (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x)))) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x))))) (+ (log (sqrt (+ 1 x))) (log (sqrt (+ 1 x))))))

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch1.0ms

end0.0ms

sample9.2s

Algorithm
intervals
Results
5.8s3466×body1280valid
2.1s2400×body640valid
596.0ms1258×body320valid
290.0ms8000×pre80true
208.0ms644×body160valid
62.0ms232×body80valid