Details

Time bar (total: 14.0s)

sample169.0ms

Algorithm
intervals
Results
88.0ms713×body80nan
13.0ms256×body80valid

simplify28.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
27.0ms
(* (sqrt (- x 1)) (sqrt x))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite393.0ms

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
390.0ms
(* (sqrt (- x 1)) (sqrt x))

series93.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
93.0ms
(* (sqrt (- x 1)) (sqrt x))

simplify1.2s

Counts
35 → 42
Calls
35 calls:
Slowest
379.0ms
(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
342.0ms
(* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x))
86.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
62.0ms
(* (sqrt (- (* x x) (* 1 1))) (sqrt x))
28.0ms
(* (- x 1) x)

prune345.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 0 expressions with local error:

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0
Calls
0 calls:
Slowest

series0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

simplify0.0ms

Counts
0 → 0
Calls
0 calls:
Slowest

prune5.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×sqrt-prod
11×*-un-lft-identity
10×associate-*l*
8×pow1 sqrt-div associate-*l/ add-cube-cbrt
6×cbrt-div add-cbrt-cube associate-*r* add-exp-log
4×expm1-log1p-u flip3-- insert-posit16 log1p-expm1-u flip-- add-log-exp unswap-sqr
3×cbrt-prod pow1/3 pow-prod-down
2×sqrt-pow1 pow1/2 difference-of-squares
1×sqrt-unprod difference-of-sqr-1 prod-exp *-commutative cbrt-unprod distribute-lft-out--
Counts
4 → 81
Calls
4 calls:
Slowest
25.0ms
(* (sqrt (- x 1)) (sqrt x))
24.0ms
(cbrt (* (sqrt (- x 1)) (sqrt x)))
16.0ms
(cbrt (* (sqrt (- x 1)) (sqrt x)))
16.0ms
(cbrt (* (sqrt (- x 1)) (sqrt x)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
170.0ms
(cbrt (* (sqrt (- x 1)) (sqrt x)))
152.0ms
(cbrt (* (sqrt (- x 1)) (sqrt x)))
145.0ms
(cbrt (* (sqrt (- x 1)) (sqrt x)))
75.0ms
(* (sqrt (- x 1)) (sqrt x))

simplify4.8s

Counts
53 → 93
Calls
53 calls:
Slowest
424.0ms
(cbrt (* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x)))
407.0ms
(- (exp (* 1/6 (+ (log -1) (log x)))) (+ (* 1/6 (* x (exp (* 1/6 (+ (log -1) (log x)))))) (* 5/72 (* (pow x 2) (exp (* 1/6 (+ (log -1) (log x))))))))
404.0ms
(cbrt (* (sqrt (- (pow x 3) (pow 1 3))) (sqrt x)))
396.0ms
(* (* (* (sqrt (- x 1)) (sqrt (- x 1))) (sqrt (- x 1))) (* (* (sqrt x) (sqrt x)) (sqrt x)))
394.0ms
(- (exp (* 1/6 (+ (log -1) (log x)))) (+ (* 1/6 (* x (exp (* 1/6 (+ (log -1) (log x)))))) (* 5/72 (* (pow x 2) (exp (* 1/6 (+ (log -1) (log x))))))))

prune958.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

27.7b
(sqrt (- (* x x) x))
0.0b
(- (* x x) x)

rewrite20.0ms

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
11.0ms
(sqrt (- (* x x) x))
9.0ms
(- (* x x) x)

series95.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
54.0ms
(- (* x x) x)
41.0ms
(sqrt (- (* x x) x))

simplify1.0s

Counts
25 → 47
Calls
25 calls:
Slowest
391.0ms
(sqrt (- (* (* x x) (* x x)) (* x x)))
186.0ms
(sqrt (- (pow (* x x) 3) (pow x 3)))
96.0ms
(- (+ (* 1/8 (/ 1 x)) 1/2) x)
93.0ms
(- x (+ (* 1/8 (/ 1 x)) 1/2))
64.0ms
(/ (exp (* x x)) (exp x))

prune266.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes96.0ms

Accuracy

0% (0.4b remaining)

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

bsearch1.0ms

end0.0ms

sample3.8s

Algorithm
intervals
Results
2.2s23839×body80nan
1.1s7992×body80valid
1.0ms8×body160valid