Details

Time bar (total: 24.8s)

sample219.0ms

Algorithm
intervals
Results
74.0ms826×body80nan
20.0ms255×body80valid
0.0ms1×body160valid

simplify31.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
30.0ms
(* (sqrt (- x 1)) (sqrt x))

prune42.0ms

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))

rewrite20.0ms

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
18.0ms
(* (sqrt (- x 1)) (sqrt x))

series100.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
100.0ms
(* (sqrt (- x 1)) (sqrt x))

simplify1.4s

Counts
35 → 42
Calls
35 calls:
Slowest
488.0ms
(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
325.0ms
(* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x))
83.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt x))
78.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
31.0ms
(+ (log (sqrt (- x 1))) (log (sqrt x)))

prune345.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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
21.0ms
(- x (- 1/2 (/ -1/8 x)))

series24.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
24.0ms
(- x (- 1/2 (/ -1/8 x)))

simplify13.3s

Counts
89 → 85
Calls
89 calls:
Slowest
447.0ms
(fma (sqrt x) (sqrt x) (- (* (- (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))) (+ (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))))))
444.0ms
(fma (- (/ -1/8 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ -1/8 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
407.0ms
(fma (- (/ -1/8 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ -1/8 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
382.0ms
(fma 1 x (- (* (- (sqrt 1/2) (sqrt (/ -1/8 x))) (+ (sqrt 1/2) (sqrt (/ -1/8 x))))))
375.0ms
(fma 1 x (- (* (- (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))) (+ (sqrt 1/2) (/ (sqrt -1/8) (sqrt x))))))

prune557.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log flip-- associate--r+ distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
Slowest
10.0ms
(- x (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))
1.0ms
(fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))

series216.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
144.0ms
(fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))
72.0ms
(- x (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))

simplify4.3s

Counts
31 → 47
Calls
31 calls:
Slowest
285.0ms
(fma (- (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))))))
265.0ms
(fma 1 x (- (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))))))
256.0ms
(fma (- (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))))))
253.0ms
(fma (- (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1))))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (* (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))) (cbrt (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))))))
237.0ms
(/ (exp x) (exp (fma (sqrt 1/2) (sqrt 1/2) (- (* (/ -1/8 x) 1)))))

prune355.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes82.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch8.0ms

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.6s23765×body80nan
618.0ms7988×body80valid
2.0ms12×body160valid