Details

Time bar (total: 2.3m)

sample107.0ms

Algorithm
intervals
Results
37.0ms234×body160nan
31.0ms528×body80nan
19.0ms256×body80valid

simplify155.0ms

Calls
1 calls:
Slowest
155.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize24.0ms

Local error

Found 3 expressions with local error:

34.1b
(sqrt (- (* x x) 1))
0.2b
(log (+ x (sqrt (- (* x x) 1))))
0.0b
(- (* x x) 1)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
25×*-un-lft-identity
20×sqrt-prod difference-of-squares
10×difference-of-sqr-1
6×swap-sqr *-commutative unswap-sqr
5×pow1 add-cube-cbrt add-log-exp
4×log-prod add-exp-log distribute-lft-out--
3×add-cbrt-cube insert-posit16
2×log-div flip3-- sqrt-div associate-*l* flip--
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ pow1/2 diff-log rem-log-exp log-pow flip-+ distribute-lft-out
Calls
3 calls:
Slowest
50.0ms
(log (+ x (sqrt (- (* x x) 1))))
25.0ms
(- (* x x) 1)
23.0ms
(sqrt (- (* x x) 1))

series329.0ms

Calls
3 calls:
Slowest
207.0ms
(log (+ x (sqrt (- (* x x) 1))))
67.0ms
(- (* x x) 1)
55.0ms
(sqrt (- (* x x) 1))

simplify3.8s

Calls
68 calls:
Slowest
507.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
406.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
243.0ms
(sqrt (- (pow (* x x) 3) (pow 1 3)))
240.0ms
(log (- (* x x) (* (sqrt (- (* x x) 1)) (sqrt (- (* x x) 1)))))
239.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))

prune586.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (sqrt (+ x 1)) (sqrt (- x 1)))
0.2b
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
16×*-un-lft-identity
15×sqrt-prod
12×sqrt-div
10×associate-*r*
8×associate-*l*
7×pow1 add-cube-cbrt
5×log-prod add-exp-log
4×frac-times flip3-+ add-cbrt-cube flip-+ unswap-sqr
3×flip3-- pow-prod-down flip-- distribute-lft-out
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--
Calls
2 calls:
Slowest
65.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
48.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

series332.0ms

Calls
2 calls:
Slowest
222.0ms
(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
110.0ms
(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify3.8s

Calls
57 calls:
Slowest
400.0ms
(log (+ (pow x 3) (pow (* (sqrt (+ x 1)) (sqrt (- x 1))) 3)))
328.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt (- (pow x 3) (pow 1 3))))
326.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
293.0ms
(log (- (* x x) (* (* (sqrt (+ x 1)) (sqrt (- x 1))) (* (sqrt (+ x 1)) (sqrt (- x 1))))))
270.0ms
(* (sqrt (+ (pow x 3) (pow 1 3))) (sqrt (- (pow x 3) (pow 1 3))))

prune666.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 1/4 (* x x))
0.7b
(/ 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))

rewrite574.0ms

Algorithm
rewrite-expression-head
Rules
1545×times-frac
1046×add-sqr-sqrt
854×*-un-lft-identity
830×add-cube-cbrt
321×swap-sqr associate-*r* associate-*l*
107×*-commutative unswap-sqr
60×associate-/r*
58×associate-/l*
35×add-cbrt-cube add-exp-log
28×add-log-exp
21×diff-log distribute-lft-out-- associate-/l/
19×div-inv
14×cbrt-undiv div-exp
10×pow1
8×associate--l+
7×prod-exp cbrt-unprod
6×log-prod log-pow
5×flip3-- flip-- associate--r+
4×clear-num frac-2neg frac-sub insert-posit16 associate--r-
3×sub-neg
1×associate--l- difference-of-squares
Calls
4 calls:
Slowest
458.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
48.0ms
(/ (/ 3/32 (* x x)) (* x x))
9.0ms
(/ 3/32 (* x x))
9.0ms
(/ 1/4 (* x x))

series287.0ms

Calls
4 calls:
Slowest
140.0ms
(- (- (log 2) (/ (/ 3/32 (* x x)) (* x x))) (- (/ 1/4 (* x x)) (log x)))
59.0ms
(/ 1/4 (* x x))
50.0ms
(/ (/ 3/32 (* x x)) (* x x))
36.0ms
(/ 3/32 (* x x))

simplify1.8m

Calls
1827 calls:
Slowest
867.0ms
(- (* (- (* (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))))
507.0ms
(- (* (- (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)))))
503.0ms
(/ (/ (* (cbrt 3/32) (cbrt 3/32)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) (* x (* (cbrt x) (cbrt x))))
459.0ms
(/ (/ (* (cbrt 3/32) (cbrt 3/32)) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x)))) x)
452.0ms
(/ (/ (* (cbrt 3/32) (cbrt 3/32)) (* x (sqrt x))) (* x (sqrt x)))

prune11.6s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes24.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.5s16121×body80nan
1.5s7800×body160nan
788.0ms8000×body80valid