Details

Time bar (total: 32.0s)

sample124.0ms

Algorithm
intervals
Results
44.0ms250×body160nan
37.0ms511×body80nan
23.0ms256×body80valid

simplify108.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
108.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize28.0ms

Local error

Found 4 expressions with local error:

29.6b
(sqrt (- (* x x) 1))
0.2b
(log (+ x (sqrt (- (* x x) 1))))
0.0b
(+ x (sqrt (- (* x x) 1)))
0.0b
(- (* x x) 1)

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
6×pow1 add-cube-cbrt sqrt-prod
5×add-exp-log
4×log-prod add-cbrt-cube insert-posit16 difference-of-squares
2×log-div flip3-+ flip3-- sqrt-div difference-of-sqr-1 flip-+ flip-- distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sub-neg sqrt-pow1 pow1/2 diff-log rem-log-exp log-pow
Counts
4 → 64
Calls
4 calls:
Slowest
14.0ms
(sqrt (- (* x x) 1))
11.0ms
(+ x (sqrt (- (* x x) 1)))
11.0ms
(log (+ x (sqrt (- (* x x) 1))))
7.0ms
(- (* x x) 1)

series387.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(log (+ x (sqrt (- (* x x) 1))))
78.0ms
(+ x (sqrt (- (* x x) 1)))
71.0ms
(- (* x x) 1)
60.0ms
(sqrt (- (* x x) 1))

simplify4.7s

Counts
37 → 76
Calls
37 calls:
Slowest
550.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
485.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
314.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
279.0ms
(log (- (* x x) (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1)))))
251.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune605.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.6b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.2b
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.0b
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
15×sqrt-prod
13×*-un-lft-identity
12×sqrt-div
10×associate-*r*
8×pow1 add-cube-cbrt
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+ add-log-exp
4×frac-times unswap-sqr
3×log-prod flip3-- pow-prod-down insert-posit16 flip--
2×log-div sqrt-pow1 pow1/2 associate-*l/ associate-*r/ difference-of-squares
1×+-commutative sum-log sqrt-unprod difference-of-sqr-1 rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
3 → 71
Calls
3 calls:
Slowest
28.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
4.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
2.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series430.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
211.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
114.0ms
(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
105.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify4.7s

Counts
59 → 80
Calls
59 calls:
Slowest
449.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
411.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
339.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
297.0ms
(log (- (* x x) (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1))))))
261.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))))

prune625.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1/4 (* x x))
0.5b
(/ 3/32 (* x x))
0.2b
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
0.1b
(/ (/ 3/32 (* x x)) (* x x))

rewrite280.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
35×add-cbrt-cube add-exp-log
21×distribute-lft-out--
19×times-frac
15×add-sqr-sqrt
14×cbrt-undiv div-exp
13×add-cube-cbrt associate-/l*
12×add-log-exp
10×pow1
8×diff-log associate--l+
7×prod-exp cbrt-unprod
6×log-pow
5×flip3-- div-inv flip--
4×frac-sub insert-posit16
3×log-prod clear-num associate-/r* sub-neg frac-2neg
2×associate--r+
1×associate--l- associate--r- difference-of-squares associate-/l/
Counts
4 → 122
Calls
4 calls:
Slowest
238.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
27.0ms
(/ (/ 3/32 (* x x)) (* x x))
6.0ms
(/ 1/4 (* x x))
6.0ms
(/ 3/32 (* x x))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
58.0ms
(/ (/ 3/32 (* x x)) (* x x))
55.0ms
(/ 1/4 (* x x))
28.0ms
(/ 3/32 (* x x))

simplify13.6s

Counts
99 → 134
Calls
99 calls:
Slowest
804.0ms
(* (+ (* (log 2) (log 2)) (+ (* (/ (/ 3/32 (* x x)) (* x x)) (/ (/ 3/32 (* x x)) (* x x))) (* (log 2) (/ (/ 3/32 (* x x)) (* x x))))) (+ (* (/ 1/4 (* x x)) (/ 1/4 (* x x))) (+ (* (log x) (log x)) (* (/ 1/4 (* x x)) (log x)))))
547.0ms
(- (* (- (* (log 2) (log 2)) (* (/ (/ 3/32 (* x x)) (* x x)) (/ (/ 3/32 (* x x)) (* x x)))) (+ (* (/ 1/4 (* x x)) (/ 1/4 (* x x))) (+ (* (log x) (log x)) (* (/ 1/4 (* x x)) (log x))))) (* (+ (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (pow (/ 1/4 (* x x)) 3) (pow (log x) 3))))
478.0ms
(- (* (- (pow (log 2) 3) (pow (/ (/ 3/32 (* x x)) (* x x)) 3)) (+ (/ 1/4 (* x x)) (log x))) (* (+ (* (log 2) (log 2)) (+ (* (/ (/ 3/32 (* x x)) (* x x)) (/ (/ 3/32 (* x x)) (* x x))) (* (log 2) (/ (/ 3/32 (* x x)) (* x x))))) (- (* (/ 1/4 (* x x)) (/ 1/4 (* x x))) (* (log x) (log x)))))
453.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
444.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch3.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.5s7461×body160nan
1.3s8000×body80valid
1.2s16101×body80nan