Details

Time bar (total: 21.4s)

sample207.0ms

Algorithm
intervals
Results
60.0ms796×body80nan
15.0ms255×body80valid
0.0ms1×body160valid

simplify20.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
20.0ms
(* (sqrt (- x 1)) (sqrt x))

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 1 expressions with local error:

0.5b
(* (sqrt (- x 1)) (sqrt x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
14×sqrt-prod
10×associate-*l*
8×*-un-lft-identity
6×associate-*r*
5×pow1 add-cube-cbrt
4×unswap-sqr
3×add-cbrt-cube pow-prod-down add-exp-log
2×sqrt-pow1 pow1/2 sqrt-div associate-*l/ difference-of-squares
1×expm1-log1p-u flip3-- sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- add-log-exp
Counts
1 → 39
Calls
1 calls:
Slowest
19.0ms
(* (sqrt (- x 1)) (sqrt x))

series81.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
80.0ms
(* (sqrt (- x 1)) (sqrt x))

simplify1.4s

Counts
35 → 42
Calls
35 calls:
Slowest
537.0ms
(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
301.0ms
(* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x))
74.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
74.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt x))
66.0ms
(+ (log (sqrt (- x 1))) (log (sqrt x)))

prune374.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b
(- x (- 1/2 (/ -1/8 x)))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
57×prod-diff
56×*-un-lft-identity
45×add-cube-cbrt
41×associate--r+
30×times-frac
7×difference-of-squares
6×distribute-lft-out-- add-log-exp
3×fma-neg diff-log div-inv
2×sub-neg
1×expm1-log1p-u pow1 flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- associate--r-
Counts
1 → 82
Calls
1 calls:
Slowest
42.0ms
(- x (- 1/2 (/ -1/8 x)))

series25.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
25.0ms
(- x (- 1/2 (/ -1/8 x)))

simplify13.4s

Counts
89 → 85
Calls
89 calls:
Slowest
473.0ms
(fma (- (/ -1/8 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ -1/8 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
473.0ms
(fma (- (/ -1/8 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ -1/8 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
406.0ms
(fma 1 x (- (* (- (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))) (+ (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))))))
405.0ms
(fma (sqrt x) (sqrt x) (- (* (- (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))) (+ (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))))))
369.0ms
(fma (- (/ -1/8 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ -1/8 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))

prune508.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

29.4b
(sqrt (- (* x x) x))
0.0b
(- (* x x) x)

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity
5×sqrt-prod
4×add-cube-cbrt add-log-exp
3×pow1 prod-diff
2×expm1-log1p-u flip3-- add-cbrt-cube distribute-rgt-out-- sqrt-div add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 fma-neg diff-log
Counts
2 → 41
Calls
2 calls:
Slowest
21.0ms
(sqrt (- (* x x) x))
14.0ms
(- (* x x) x)

series74.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
42.0ms
(- (* x x) x)
32.0ms
(sqrt (- (* x x) x))

simplify1.1s

Counts
25 → 47
Calls
25 calls:
Slowest
466.0ms
(sqrt (- (* (* x x) (* x x)) (* x x)))
196.0ms
(sqrt (- (pow (* x x) 3) (pow x 3)))
94.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
88.0ms
(- (+ (* 1/8 (/ 1 x)) 1/2) x)
76.0ms
(/ (exp (* x x)) (exp x))

prune260.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes46.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch1.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.6s24077×body80nan
547.0ms7989×body80valid
1.0ms11×body160valid