Details

Time bar (total: 13.0s)

sample97.0ms

Algorithm
intervals
Results
37.0ms509×body80nan
28.0ms255×body160nan
16.0ms256×body80valid

simplify134.0ms

Calls
1 calls:
Slowest
134.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize11.0ms

Local error

Found 3 expressions with local error:

29.5b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))
0.0b
(log (+ x (sqrt (fma x x -1))))

rewrite4.0ms

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

series149.0ms

Calls
3 calls:
Slowest
82.0ms
(log (+ x (sqrt (fma x x -1))))
35.0ms
(sqrt (fma x x -1))
32.0ms
(+ x (sqrt (fma x x -1)))

simplify2.8s

Calls
19 calls:
Slowest
501.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
410.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
315.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
227.0ms
(- (+ (log (sqrt -1)) (/ x (sqrt -1))) (* 1/6 (/ (pow x 3) (pow (sqrt -1) 3))))
204.0ms
(log (- (* x x) (* (sqrt (fma x x -1)) (sqrt (fma x x -1)))))

prune421.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

1.0b
(/ -1/8 (* x x))
0.1b
(/ (/ -1/8 (* x x)) x)
0.0b
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×associate-/l*
3×expm1-log1p-u pow1 fma-def add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv
2×clear-num frac-2neg
1×+-commutative associate-+l+ associate-/r* sum-log flip3-+ flip-+ fma-udef distribute-lft-out associate-/l/
Calls
3 calls:
Slowest
10.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
3.0ms
(/ (/ -1/8 (* x x)) x)
0.0ms
(/ -1/8 (* x x))

series62.0ms

Calls
3 calls:
Slowest
23.0ms
(/ -1/8 (* x x))
21.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
17.0ms
(/ (/ -1/8 (* x x)) x)

simplify1.0s

Calls
16 calls:
Slowest
233.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
225.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
216.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
138.0ms
(* (exp (fma 2 x (/ -1/2 x))) (exp (/ (/ -1/8 (* x x)) x)))
38.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))

prune543.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

29.5b
(sqrt (fma x x -1))
29.5b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×+-commutative rem-sqrt-square flip3-+ pow1/2 flip-+
Calls
4 calls:
Slowest
2.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(sqrt (fma x x -1))
2.0ms
(sqrt (fma x x -1))

series145.0ms

Calls
4 calls:
Slowest
45.0ms
(+ x (sqrt (fma x x -1)))
44.0ms
(+ x (sqrt (fma x x -1)))
34.0ms
(sqrt (fma x x -1))
21.0ms
(sqrt (fma x x -1))

simplify2.4s

Calls
20 calls:
Slowest
277.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
271.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
254.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
246.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
243.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))

prune741.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes27.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch1.0ms

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.8s7744×body160nan
1.5s16315×body80nan
698.0ms8000×body80valid