Details

Time bar (total: 25.8s)

sample127.0ms

Algorithm
intervals
Results
55.0ms523×body80nan
33.0ms249×body160nan
22.0ms256×body80valid

simplify117.0ms

Calls
1 calls:
Slowest
117.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.2b

localize24.0ms

Local error

Found 2 expressions with local error:

28.0b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite12.0ms

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
Calls
2 calls:
Slowest
9.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(sqrt (fma x x -1))

series144.0ms

Calls
2 calls:
Slowest
86.0ms
(+ x (sqrt (fma x x -1)))
58.0ms
(sqrt (fma x x -1))

simplify1.7s

Calls
15 calls:
Slowest
475.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
297.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
256.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
233.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
204.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune324.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 1 expressions with local error:

0.1b
(/ (/ -1/8 x) (* x x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
339×times-frac
213×add-sqr-sqrt
185×*-un-lft-identity add-cube-cbrt
42×swap-sqr associate-*r* associate-*l*
18×associate-/r*
17×div-inv
16×associate-/l*
14×*-commutative unswap-sqr
13×add-cbrt-cube add-exp-log
9×associate-/l/
6×cbrt-undiv div-exp
2×clear-num frac-2neg prod-exp cbrt-unprod
1×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
Calls
1 calls:
Slowest
12.0ms
(/ (/ -1/8 x) (* x x))

series75.0ms

Calls
1 calls:
Slowest
75.0ms
(/ (/ -1/8 x) (* x x))

simplify16.7s

Calls
430 calls:
Slowest
446.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))
428.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) 1) (* (* (cbrt x) (cbrt x)) (* (cbrt x) (cbrt x))))
388.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) (* (cbrt (* x x)) (cbrt (* x x))))
362.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) 1) (* x (* (cbrt x) (cbrt x))))
352.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) (* x (sqrt x)))

prune2.2s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes21.0ms

Accuracy

0% (0.2b remaining)

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

bsearch1.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.5s7615×body160nan
1.3s8000×body80valid
1.2s16087×body80nan