Details

Time bar (total: 28.5s)

sample98.0ms

Algorithm
intervals
Results
34.0ms262×body160nan
27.0ms542×body80nan
18.0ms256×body80valid

simplify144.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
144.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize25.0ms

Local error

Found 3 expressions with local error:

26.3b
(sqrt (- (* x x) 1))
0.2b
(log (+ x (sqrt (- (* x x) 1))))
0.0b
(- (* x x) 1)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
8×add-sqr-sqrt
6×sqrt-prod
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log difference-of-squares
3×add-cbrt-cube insert-posit16
2×log-div flip3-- sqrt-div difference-of-sqr-1 flip--
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log rem-log-exp log-pow flip-+ distribute-lft-out
Counts
3 → 51
Calls
3 calls:
Slowest
20.0ms
(log (+ x (sqrt (- (* x x) 1))))
14.0ms
(sqrt (- (* x x) 1))
12.0ms
(- (* x x) 1)

series310.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
181.0ms
(log (+ x (sqrt (- (* x x) 1))))
70.0ms
(- (* x x) 1)
59.0ms
(sqrt (- (* x x) 1))

simplify3.2s

Counts
32 → 60
Calls
32 calls:
Slowest
425.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
377.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
260.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
210.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
192.0ms
(log (+ (pow x 3) (pow (sqrt (- (* x x) 1)) 3)))

prune493.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 2 expressions with local error:

0.5b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.2b
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×sqrt-prod
12×*-un-lft-identity sqrt-div
10×associate-*r*
7×pow1 associate-*l* add-cube-cbrt
5×add-exp-log
4×frac-times flip3-+ add-cbrt-cube flip-+ unswap-sqr
3×log-prod flip3-- pow-prod-down flip--
2×log-div sqrt-pow1 pow1/2 associate-*l/ associate-*r/ insert-posit16 add-log-exp difference-of-squares
1×sqrt-unprod difference-of-sqr-1 rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out distribute-lft-out--
Counts
2 → 59
Calls
2 calls:
Slowest
29.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))
3.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

series267.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
167.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
100.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify3.8s

Counts
55 → 65
Calls
55 calls:
Slowest
374.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
354.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
303.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))
299.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
289.0ms
(log (- (* x x) (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1))))))

prune620.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1/4 (* x x))
0.6b
(/ 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))

rewrite273.0ms

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
225.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
28.0ms
(/ (/ 3/32 (* x x)) (* x x))
11.0ms
(/ 1/4 (* x x))
6.0ms
(/ 3/32 (* x x))

series305.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
147.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
54.0ms
(/ (/ 3/32 (* x x)) (* x x))
52.0ms
(/ 3/32 (* x x))
51.0ms
(/ 1/4 (* x x))

simplify12.6s

Counts
99 → 134
Calls
99 calls:
Slowest
540.0ms
(- (* (- (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)))))
468.0ms
(* (+ (* (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)))))
450.0ms
(- (* (- (* (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))))
428.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
405.0ms
(/ (* (* 3/32 3/32) 3/32) (* (* (* x x) x) (* (* x x) x)))

prune1.3s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm
intervals
Results
2.2s7896×body160nan
1.4s16517×body80nan
835.0ms8000×body80valid