Details

Time bar (total: 7.9s)

sample111.0ms

Algorithm
intervals
Results
36.0ms234×body160nan
33.0ms514×body80nan
24.0ms256×body80valid

simplify128.0ms

Calls
1 calls:
Slowest
127.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize22.0ms

Local error

Found 2 expressions with local error:

30.4b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite5.0ms

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

series150.0ms

Calls
2 calls:
Slowest
93.0ms
(+ x (sqrt (fma x x -1)))
57.0ms
(sqrt (fma x x -1))

simplify1.0s

Calls
10 calls:
Slowest
266.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
201.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
137.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
125.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
121.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune263.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 3 expressions with local error:

0.4b
(/ -1/8 (* x x))
0.1b
(/ (/ -1/8 (* x x)) x)
0.0b
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))

rewrite19.0ms

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
11.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
7.0ms
(/ (/ -1/8 (* x x)) x)
1.0ms
(/ -1/8 (* x x))

series169.0ms

Calls
3 calls:
Slowest
68.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
53.0ms
(/ (/ -1/8 (* x x)) x)
48.0ms
(/ -1/8 (* x x))

simplify1.2s

Calls
16 calls:
Slowest
281.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
259.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
231.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
159.0ms
(* (exp (fma 2 x (/ -1/2 x))) (exp (/ (/ -1/8 (* x x)) x)))
49.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))

prune604.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.8s7557×body160nan
1.2s16003×body80nan
780.0ms8000×body80valid