Details

Time bar (total: 3.7m)

sample108.0ms

Algorithm
intervals
Results
48.0ms234×body160nan
28.0ms528×body80nan
17.0ms256×body80valid

simplify112.0ms

Calls
1 calls:
Slowest
112.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize24.0ms

Local error

Found 2 expressions with local error:

34.1b
(sqrt (fma x x -1))
0.2b
(log (+ x (sqrt (fma x x -1))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 log-prod add-cube-cbrt
3×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 sqrt-pow1 flip3-+ pow1/2 rem-log-exp log-pow flip-+ distribute-lft-out
Calls
2 calls:
Slowest
8.0ms
(log (+ x (sqrt (fma x x -1))))
2.0ms
(sqrt (fma x x -1))

series259.0ms

Calls
2 calls:
Slowest
173.0ms
(log (+ x (sqrt (fma x x -1))))
86.0ms
(sqrt (fma x x -1))

simplify2.9s

Calls
18 calls:
Slowest
819.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
439.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
363.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
269.0ms
(log (- (* x x) (* (sqrt (fma x x -1)) (sqrt (fma x x -1)))))
217.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune367.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ -1 (* x x))
0.3b
(/ 3/32 (* (* x x) (* x x)))
0.2b
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
0.1b
(* (* x x) (* x x))

rewrite796.0ms

Algorithm
rewrite-expression-head
Rules
2815×add-sqr-sqrt
1408×times-frac
1194×*-un-lft-identity
1160×prod-diff
1103×add-cube-cbrt
993×associate--r+
869×swap-sqr
857×unswap-sqr
505×associate-*l*
471×associate-*r*
415×pow1
353×*-commutative
300×log-pow
153×difference-of-squares
96×associate-/r*
39×add-cbrt-cube add-exp-log
36×pow-prod-up
23×pow-prod-down
22×pow-sqr
18×pow-plus distribute-lft-out--
17×prod-exp cbrt-unprod
15×add-log-exp
13×pow2
10×diff-log
7×cbrt-undiv div-exp
6×log-prod div-inv associate-/l*
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u associate--r-
3×associate--l+
2×clear-num sub-neg frac-2neg
1×flip3-- flip--
Calls
4 calls:
Slowest
514.0ms
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
73.0ms
(* (* x x) (* x x))
59.0ms
(/ 3/32 (* (* x x) (* x x)))
17.0ms
(/ -1 (* x x))

series2.5s

Calls
4 calls:
Slowest
2.4s
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
61.0ms
(* (* x x) (* x x))
60.0ms
(/ 3/32 (* (* x x) (* x x)))
48.0ms
(/ -1 (* x x))

simplify2.8m

Calls
2231 calls:
Slowest
695.0ms
(fma (sqrt (log 2)) (sqrt (log 2)) (- (* (- (/ (sqrt 3/32) (* x (sqrt (* x x)))) (sqrt (log x))) (+ (/ (sqrt 3/32) (* x (sqrt (* x x)))) (sqrt (log x))))))
664.0ms
(fma (- (- (/ (sqrt 3/32) (* (sqrt (* x x)) (* (sqrt x) (sqrt x)))) (sqrt (log x)))) (+ (/ (sqrt 3/32) (* (sqrt (* x x)) (* (sqrt x) (sqrt x)))) (sqrt (log x))) (* (- (/ (sqrt 3/32) (* (sqrt (* x x)) (* (sqrt x) (sqrt x)))) (sqrt (log x))) (+ (/ (sqrt 3/32) (* (sqrt (* x x)) (* (sqrt x) (sqrt x)))) (sqrt (log x)))))
658.0ms
(fma (* (cbrt (log 2)) (cbrt (log 2))) (cbrt (log 2)) (- (* (- (/ (sqrt 3/32) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x)))) (sqrt (log x))) (+ (/ (sqrt 3/32) (* (* (sqrt x) (sqrt x)) (* (sqrt x) (sqrt x)))) (sqrt (log x))))))
571.0ms
(fma (- (sqrt (- (/ 3/32 (* (* x x) (* x x))) (log x)))) (sqrt (- (/ 3/32 (* (* x x) (* x x))) (log x))) (* (sqrt (- (/ 3/32 (* (* x x) (* x x))) (log x))) (sqrt (- (/ 3/32 (* (* x x) (* x x))) (log x)))))
480.0ms
(fma (* (cbrt (log 2)) (cbrt (log 2))) (cbrt (log 2)) (- (* (- (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))) (+ (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))))))

prune23.8s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize46.0ms

Local error

Found 2 expressions with local error:

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

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
339×times-frac
215×add-sqr-sqrt
196×*-un-lft-identity
187×add-cube-cbrt
42×swap-sqr associate-*r* associate-*l*
18×associate-/r*
17×div-inv
16×associate-/l*
15×add-exp-log
14×add-cbrt-cube *-commutative unswap-sqr
9×associate-/l/
6×cbrt-undiv log-prod div-exp
3×pow1 distribute-lft-out distribute-lft-out--
2×expm1-log1p-u log-div clear-num frac-2neg prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
1×flip3-+ rem-log-exp log-pow flip-+
Calls
2 calls:
Slowest
184.0ms
(log (+ x (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x))))
26.0ms
(/ (/ -1/8 x) (* x x))

series214.0ms

Calls
2 calls:
Slowest
161.0ms
(log (+ x (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x))))
53.0ms
(/ (/ -1/8 x) (* x x))

simplify19.6s

Calls
442 calls:
Slowest
871.0ms
(log (+ (pow x 3) (pow (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x)) 3)))
456.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))
439.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
414.0ms
(log (- (* x x) (* (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x)) (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x)))))
381.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) 1) (* x (* (cbrt x) (cbrt x))))

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes19.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.7s7800×body160nan
1.1s16121×body80nan
750.0ms8000×body80valid