Details

Time bar (total: 3.2m)

sample86.0ms

Algorithm
intervals
Results
23.0ms67×body640valid
19.0ms271×body80nan
13.0ms32×body1280valid
11.0ms129×body80valid
4.0ms18×body320valid
2.0ms10×body160valid

simplify37.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
36.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.5b

localize15.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
1063×times-frac
902×*-un-lft-identity
788×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
580×sqrt-prod
74×distribute-lft-out
56×div-inv
48×sqrt-div
46×associate-/r/
25×difference-of-squares
24×flip3-+ flip-+
22×fma-neg
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube
6×pow-flip associate-/l* add-log-exp
4×expm1-log1p-u div-exp insert-posit16 log1p-expm1-u
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg 1-exp hypot-def inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Counts
4 → 793
Calls
4 calls:
Slowest
35.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
5.0ms
(sqrt (+ x 1))

series219.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
108.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
42.0ms
(/ 1 (sqrt (+ x 1)))
41.0ms
(/ 1 (sqrt x))
27.0ms
(sqrt (+ x 1))

simplify2.2m

Counts
1414 → 805
Calls
1414 calls:
Slowest
665.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (/ (cbrt 1) (sqrt (cbrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
461.0ms
(fma (- (/ (sqrt 1) (sqrt (sqrt (+ x 1))))) (/ (sqrt 1) (sqrt (sqrt (+ x 1)))) (* (/ (sqrt 1) (sqrt (sqrt (+ x 1)))) (/ (sqrt 1) (sqrt (sqrt (+ x 1))))))
450.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
396.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt x))) (/ (cbrt 1) (sqrt (sqrt x))) (- (* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))))))
395.0ms
(fma (- (/ (cbrt 1) (cbrt (sqrt (+ x 1))))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

prune5.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 18.9b

localize16.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (sqrt (+ x 1)) (sqrt x))
0.2b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
88×sqrt-prod
79×*-un-lft-identity
75×add-sqr-sqrt
42×prod-diff
39×add-cube-cbrt
12×distribute-lft-out difference-of-squares
11×add-cbrt-cube add-exp-log
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×fma-neg associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ insert-posit16 log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod hypot-def flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
4 → 171
Calls
4 calls:
Slowest
64.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
34.0ms
(- (sqrt (+ x 1)) (sqrt x))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))
5.0ms
(sqrt (+ x 1))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
152.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
61.0ms
(- (sqrt (+ x 1)) (sqrt x))
60.0ms
(* (sqrt x) (sqrt (+ x 1)))
29.0ms
(sqrt (+ x 1))

simplify5.5s

Counts
193 → 183
Calls
193 calls:
Slowest
196.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
173.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
138.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))
135.0ms
(/ (* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x))) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
130.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.2b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
31×*-un-lft-identity
23×sqrt-prod
21×add-sqr-sqrt
20×add-cbrt-cube
19×pow1
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×associate-*r* prod-exp add-cube-cbrt
10×distribute-lft-out
9×pow-prod-down
8×frac-times associate-/r/
7×fma-def associate-*l* cbrt-unprod
6×div-exp add-log-exp
4×expm1-log1p-u associate-*l/ insert-posit16 log1p-expm1-u unswap-sqr
3×cbrt-undiv rec-exp times-frac 1-exp pow-flip associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log frac-2neg distribute-lft-in sqrt-unprod div-inv inv-pow
Counts
4 → 138
Calls
4 calls:
Slowest
90.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
71.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
22.0ms
(+ (sqrt (+ x 1)) (sqrt x))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))

series503.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
203.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
182.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
61.0ms
(* (sqrt x) (sqrt (+ x 1)))
57.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify6.0s

Counts
109 → 150
Calls
109 calls:
Slowest
308.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
306.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
286.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))) (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))) (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))))
284.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
261.0ms
(/ (* (* 1 1) 1) (* (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))

prune983.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
0.1b
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
0.1b
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
795×times-frac
557×*-un-lft-identity
519×add-sqr-sqrt
425×sqrt-prod
353×add-cube-cbrt
166×associate-*l*
95×distribute-lft-out
61×cbrt-prod
54×add-exp-log
44×unswap-sqr
42×associate-*r*
36×associate-/l*
32×associate-/r/
30×add-cbrt-cube
28×sqrt-div
26×div-exp
19×associate-/r*
18×div-inv
16×flip3-+ flip-+
14×cbrt-undiv
10×prod-exp
8×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg pow-flip
1×frac-times sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative inv-pow associate-/l/
Counts
4 → 617
Calls
4 calls:
Slowest
91.0ms
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
26.0ms
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
16.0ms
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
9.0ms
(/ 1 (sqrt (+ x 1)))

series386.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
215.0ms
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
72.0ms
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
63.0ms
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
37.0ms
(/ 1 (sqrt (+ x 1)))

simplify31.6s

Counts
835 → 629
Calls
835 calls:
Slowest
598.0ms
(* (* (* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (/ 1 (sqrt (+ x 1))) (sqrt x))) (/ (/ 1 (sqrt (+ x 1))) (sqrt x))) (* (* (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))))
408.0ms
(/ (/ 1 (sqrt (+ (pow x 3) (pow 1 3)))) (sqrt (sqrt x)))
258.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (cbrt (sqrt x)) (cbrt (sqrt x))))
257.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (cbrt (sqrt x)) (cbrt (sqrt x))))
223.0ms
(+ (- (- (log (sqrt (+ x 1)))) (log (sqrt x))) (- (log (cbrt 1)) (log (+ (sqrt (+ x 1)) (sqrt x)))))

prune4.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch1.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
780.0ms8063×body80nan
526.0ms1837×body640valid
492.0ms1157×body1280valid
305.0ms4059×body80valid
130.0ms606×body320valid
40.0ms341×body160valid