Details

Time bar (total: 12.1s)

sample121.0ms

Algorithm
intervals
Results
42.0ms272×body160nan
38.0ms577×body80nan
21.0ms256×body80valid

simplify553.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
553.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize23.0ms

Local error

Found 2 expressions with local error:

26.7b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×add-cube-cbrt add-log-exp
3×pow1 fma-def sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
2 → 34
Calls
2 calls:
Slowest
10.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(sqrt (fma x x -1))

series181.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(+ x (sqrt (fma x x -1)))
83.0ms
(sqrt (fma x x -1))

simplify1.7s

Counts
15 → 40
Calls
15 calls:
Slowest
489.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
303.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
298.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
224.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
172.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
19×*-un-lft-identity
17×add-sqr-sqrt add-cube-cbrt
14×add-cbrt-cube add-exp-log
13×associate-/l*
6×cbrt-undiv div-exp
4×add-log-exp
3×fma-def div-inv
2×expm1-log1p-u pow1 prod-exp cbrt-unprod insert-posit16 log1p-expm1-u
1×+-commutative associate-+l+ clear-num associate-/r* sum-log frac-2neg flip3-+ flip-+ fma-udef distribute-lft-out associate-/l/
Counts
2 → 68
Calls
2 calls:
Slowest
16.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
10.0ms
(/ (/ -1/8 x) (* x x))

series130.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
75.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
55.0ms
(/ (/ -1/8 x) (* x x))

simplify2.7s

Counts
56 → 74
Calls
56 calls:
Slowest
235.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
235.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
195.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
182.0ms
(* (exp (fma 2 x (/ -1/2 x))) (exp (/ (/ -1/8 x) (* x x))))
160.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) x)

prune643.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 2 expressions with local error:

26.7b
(sqrt (fma x x -1))
0.1b
(fma (sqrt x) (sqrt x) (sqrt (fma x x -1)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt
3×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
2 → 27
Calls
2 calls:
Slowest
2.0ms
(sqrt (fma x x -1))
0.0ms
(fma (sqrt x) (sqrt x) (sqrt (fma x x -1)))

series207.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
138.0ms
(fma (sqrt x) (sqrt x) (sqrt (fma x x -1)))
69.0ms
(sqrt (fma x x -1))

simplify955.0ms

Counts
11 → 33
Calls
11 calls:
Slowest
485.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
204.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
179.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
51.0ms
(sqrt (* (cbrt (fma x x -1)) (cbrt (fma x x -1))))
19.0ms
(sqrt (sqrt (fma x x -1)))

prune311.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.8s16758×body80nan
1.3s7996×body160nan
704.0ms8000×body80valid