Details

Time bar (total: 29.0s)

sample97.0ms

Algorithm
intervals
Results
32.0ms252×body160nan
30.0ms534×body80nan
18.0ms256×body80valid

simplify133.0ms

Calls
1 calls:
Slowest
133.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize17.0ms

Local error

Found 2 expressions with local error:

30.4b
(sqrt (fma x x -1))
0.2b
(log (+ x (sqrt (fma x x -1))))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
4×*-un-lft-identity add-cube-cbrt
3×pow1 log-prod add-exp-log sqrt-prod
2×expm1-log1p-u log-div add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square flip3-+ pow1/2 rem-log-exp log-pow flip-+
Calls
2 calls:
Slowest
1.0ms
(log (+ x (sqrt (fma x x -1))))
1.0ms
(sqrt (fma x x -1))

series199.0ms

Calls
2 calls:
Slowest
150.0ms
(log (+ x (sqrt (fma x x -1))))
49.0ms
(sqrt (fma x x -1))

simplify2.0s

Calls
16 calls:
Slowest
353.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
347.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
285.0ms
(+ (log (sqrt -1)) (+ (/ x (sqrt -1)) (+ (* 1/2 (/ (pow x 3) (sqrt -1))) (* 1/3 (/ (pow x 3) (pow (sqrt -1) 3))))))
219.0ms
(log (- (* x x) (* (sqrt (fma x x -1)) (sqrt (fma x x -1)))))
161.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune238.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 3/32 (pow x 4))
0.2b
(+ (log x) (log 2))
0.2b
(/ (/ -1/4 x) x)
0.0b
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
19×associate-+l+
18×add-sqr-sqrt
16×prod-diff add-cube-cbrt
11×add-log-exp
10×distribute-lft-out
9×fma-def
7×div-inv
5×sum-log
4×expm1-log1p-u pow1 add-cbrt-cube frac-add add-exp-log insert-posit16 log1p-expm1-u associate-/l* distribute-lft-out--
3×associate-/r* flip3-+ flip-+
2×+-commutative clear-num frac-2neg diff-log frac-sub
1×sub-neg flip3-- associate--l+ associate-+l- flip-- difference-of-squares associate-/l/
Calls
4 calls:
Slowest
130.0ms
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))
5.0ms
(+ (log x) (log 2))
3.0ms
(/ (/ -1/4 x) x)
1.0ms
(/ 3/32 (pow x 4))

series500.0ms

Calls
4 calls:
Slowest
321.0ms
(+ (log x) (log 2))
102.0ms
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))
50.0ms
(/ 3/32 (pow x 4))
26.0ms
(/ (/ -1/4 x) x)

simplify5.6s

Calls
58 calls:
Slowest
385.0ms
(+ (* (- (* (- (* (log x) (log x)) (* (log 2) (log 2))) (pow x 4)) (* (- (log x) (log 2)) 3/32)) x) (* (* (- (log x) (log 2)) (pow x 4)) (/ -1/4 x)))
369.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
369.0ms
(- (+ (log 2) (log -1)) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
280.0ms
(* (/ (exp (+ (log x) (log 2))) (exp (/ 3/32 (pow x 4)))) (exp (/ (/ -1/4 x) x)))
255.0ms
(* (exp (- (+ (log x) (log 2)) (/ 3/32 (pow x 4)))) (exp (/ (/ -1/4 x) x)))

prune1.3s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (+ x (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x))))
0.1b
(/ (/ 1/8 x) (* x x))
0.0b
(+ x (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x)))
0.0b
(- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity prod-diff
22×add-cube-cbrt
15×associate-+r+
10×div-inv
7×add-exp-log
6×add-cbrt-cube add-log-exp
5×pow1
4×expm1-log1p-u times-frac fma-neg insert-posit16 log1p-expm1-u associate-/l*
3×log-prod sub-neg
2×log-div flip3-+ flip3-- frac-sub flip-+ flip-- associate--r+ associate--r-
1×cbrt-undiv +-commutative clear-num associate-+r- associate-/r* frac-2neg diff-log div-exp rem-log-exp log-pow distribute-lft-out-- difference-of-squares associate-/l/
Calls
4 calls:
Slowest
29.0ms
(+ x (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x)))
28.0ms
(log (+ x (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x))))
23.0ms
(- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x))
8.0ms
(/ (/ 1/8 x) (* x x))

series308.0ms

Calls
4 calls:
Slowest
145.0ms
(log (+ x (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x))))
59.0ms
(+ x (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x)))
55.0ms
(/ (/ 1/8 x) (* x x))
49.0ms
(- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x))

simplify13.1s

Calls
81 calls:
Slowest
801.0ms
(log (+ (pow x 3) (pow (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x)) 3)))
734.0ms
(- (* -1/2 (+ (/ (/ 1/8 x) (* x x)) x)) (* x (- (* (/ (/ 1/8 x) (* x x)) (/ (/ 1/8 x) (* x x))) (* x x))))
583.0ms
(* x (+ (* (/ (/ 1/8 x) (* x x)) (/ (/ 1/8 x) (* x x))) (+ (* x x) (* (/ (/ 1/8 x) (* x x)) x))))
431.0ms
(- (+ (log -1/8) (* 4 (pow x 2))) (+ (* 24 (pow x 4)) (* 3 (log x))))
402.0ms
(log (- (* x x) (* (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x)) (- (/ -1/2 x) (- (/ (/ 1/8 x) (* x x)) x)))))

prune1.0s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch5.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.8s7791×body160nan
1.2s16249×body80nan
815.0ms8000×body80valid