Details

Time bar (total: 42.4s)

sample254.0ms

Algorithm
intervals
Results
149.0ms101×body1280valid
62.0ms89×body640valid
16.0ms40×body320valid
9.0ms256×pre80true
5.0ms16×body160valid
1.0ms10×body80valid

simplify20.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
20.0ms
(/ (log (- 1 x)) (log (+ 1 x)))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.3b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite37.0ms

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
29.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
3.0ms
(log (- 1 x))
3.0ms
(log (+ 1 x))

series144.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
85.0ms
(/ (log (- 1 x)) (log (+ 1 x)))
32.0ms
(log (+ 1 x))
27.0ms
(log (- 1 x))

simplify4.6s

Counts
67 → 82
Calls
67 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)))))))))))
529.0ms
(/ (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))) (* (* (log (+ 1 x)) (log (+ 1 x))) (log (+ 1 x))))
394.0ms
(- (+ (/ 1 x) (log -1)) (+ (log (/ -1 x)) (* 1/2 (/ 1 (pow x 2)))))
392.0ms
(- (+ (* 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)))))
387.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite57.0ms

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))
15.0ms
(* (* x x) -1/2)

series65.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
38.0ms
(* (* x x) -1/2)
27.0ms
(+ (- -1 x) (* (* x x) -1/2))

simplify1.6s

Counts
18 → 42
Calls
18 calls:
Slowest
334.0ms
(* (* (* (* x x) (* x x)) (* x x)) (* (* -1/2 -1/2) -1/2))
266.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* -1/2 -1/2) -1/2))
183.0ms
(* (/ (exp -1) (exp x)) (exp (* (* x x) -1/2)))
162.0ms
(- (+ x (+ (* 1/2 (pow x 2)) 1)))
161.0ms
(* (exp (- -1 x)) (exp (* (* x x) -1/2)))

prune258.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
140×times-frac
78×*-un-lft-identity
76×add-sqr-sqrt
73×add-cube-cbrt
49×pow1
44×log-pow
24×associate-/r*
19×add-exp-log
11×add-cbrt-cube
10×log-prod
8×div-exp
7×associate-/l*
6×log-div div-inv
4×cbrt-undiv insert-posit16 add-log-exp
2×rec-exp clear-num frac-2neg flip3-+ 1-exp div-sub rem-log-exp flip-+ difference-of-squares
1×flip3-- associate-/r/ pow-flip flip-- distribute-lft-out distribute-lft-out-- inv-pow
Counts
4 → 178
Calls
4 calls:
Slowest
12.0ms
(/ 1 (/ (log (+ 1 x)) (log (- 1 x))))
11.0ms
(/ (log (+ 1 x)) (log (- 1 x)))
3.0ms
(log (- 1 x))
3.0ms
(log (+ 1 x))

series254.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ 1 (/ (log (+ 1 x)) (log (- 1 x))))
87.0ms
(/ (log (+ 1 x)) (log (- 1 x)))
29.0ms
(log (- 1 x))
22.0ms
(log (+ 1 x))

simplify14.2s

Counts
220 → 190
Calls
220 calls:
Slowest
888.0ms
(- (+ (/ (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)))))))))))
578.0ms
(- (+ (/ 1 (* (pow x 2) (pow (- (log -1) (log (/ 1 x))) 2))) (/ 1 (* x (- (log -1) (log (/ 1 x)))))) (+ (/ (log (/ 1 x)) (- (log -1) (log (/ 1 x)))) (+ (* 1/2 (/ 1 (* (pow x 2) (- (log -1) (log (/ 1 x)))))) (+ (/ (log (/ 1 x)) (* (pow (- (log -1) (log (/ 1 x))) 2) x)) (+ (/ (log (/ 1 x)) (* (pow (- (log -1) (log (/ 1 x))) 3) (pow x 2))) (* 1/2 (/ (log (/ 1 x)) (* (pow (- (log -1) (log (/ 1 x))) 2) (pow x 2)))))))))
519.0ms
(- (+ (* 1/2 (/ (log -1) (* (pow x 2) (pow (log (/ -1 x)) 2)))) (+ (* 2 (/ 1 (* (pow x 2) (pow (log (/ -1 x)) 2)))) (+ (/ (log -1) (* x (pow (log (/ -1 x)) 2))) 1))) (+ (/ (log -1) (* (pow x 2) (pow (log (/ -1 x)) 3))) (+ (/ (log -1) (log (/ -1 x))) (* 2 (/ 1 (* x (log (/ -1 x))))))))
482.0ms
(/ (* (* (log (+ 1 x)) (log (+ 1 x))) (log (+ 1 x))) (* (* (log (- 1 x)) (log (- 1 x))) (log (- 1 x))))
471.0ms
(/ (* (* 1 1) 1) (* (* (/ (log (+ 1 x)) (log (- 1 x))) (/ (log (+ 1 x)) (log (- 1 x)))) (/ (log (+ 1 x)) (log (- 1 x)))))

prune1.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

5.3b
(log (- 1 x))
5.3b
(log (- 1 x))
2.4b
(log (- 1 (* x x)))
0.0b
(/ (log (- 1 x)) (- (log (- 1 (* x x))) (log (- 1 x))))

rewrite48.0ms

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
35.0ms
(/ (log (- 1 x)) (- (log (- 1 (* x x))) (log (- 1 x))))
4.0ms
(log (- 1 x))
4.0ms
(log (- 1 x))
3.0ms
(log (- 1 (* x x)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
154.0ms
(/ (log (- 1 x)) (- (log (- 1 (* x x))) (log (- 1 x))))
130.0ms
(log (- 1 (* x x)))
42.0ms
(log (- 1 x))
33.0ms
(log (- 1 x))

simplify7.6s

Counts
118 → 126
Calls
118 calls:
Slowest
844.0ms
(- (+ (/ (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)))))))))))
473.0ms
(- (+ (* 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)))))
449.0ms
(- (+ (pow x 2) (+ (* 1/2 (pow x 4)) (* 1/3 (pow x 6)))))
420.0ms
(- (+ (log (/ -1 x)) (+ (* 1/2 (/ 1 (pow x 2))) (/ 1 x))))
388.0ms
(/ (log (- (pow 1 3) (pow x 3))) (- (log (- 1 (* x x))) (log (- 1 x))))

prune814.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes43.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample9.5s

Algorithm
intervals
Results
5.9s3448×body1280valid
2.1s2498×body640valid
585.0ms1211×body320valid
357.0ms8000×pre80true
231.0ms623×body160valid
53.0ms220×body80valid