Details

Time bar (total: 2.4m)

sample113.0ms

Algorithm
intervals
Results
23.0ms54×body640valid
20.0ms37×body1280valid
19.0ms20×body320valid
18.0ms207×body80nan
14.0ms138×body80valid
2.0ms7×body160valid

simplify37.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
37.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize20.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite126.0ms

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
41.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
16.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt x))
8.0ms
(sqrt (+ x 1))

series192.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
82.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
46.0ms
(/ 1 (sqrt (+ x 1)))
40.0ms
(/ 1 (sqrt x))
24.0ms
(sqrt (+ x 1))

simplify1.8m

Counts
1414 → 805
Calls
1414 calls:
Slowest
493.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt x))) (/ (cbrt 1) (sqrt (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
435.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (/ (cbrt 1) (sqrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (sqrt (sqrt (+ x 1)))))))
398.0ms
(fma (/ 1 1) (/ 1 (sqrt x)) (- (* (/ (sqrt 1) (cbrt (sqrt (+ x 1)))) (/ (sqrt 1) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
395.0ms
(fma (* (cbrt (/ 1 (sqrt x))) (cbrt (/ 1 (sqrt x)))) (cbrt (/ 1 (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
346.0ms
(fma (- (/ 1 (cbrt (sqrt (+ x 1))))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (/ 1 (cbrt (sqrt (+ x 1)))) (/ 1 (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1)))))))

prune4.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.9b

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite107.0ms

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
56.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
27.0ms
(- (sqrt (+ x 1)) (sqrt x))
17.0ms
(* (sqrt x) (sqrt (+ x 1)))
4.0ms
(sqrt (+ x 1))

series265.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
52.0ms
(* (sqrt x) (sqrt (+ x 1)))
52.0ms
(- (sqrt (+ x 1)) (sqrt x))
22.0ms
(sqrt (+ x 1))

simplify5.1s

Counts
193 → 183
Calls
193 calls:
Slowest
180.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
161.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
126.0ms
(/ (* (* (- (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)))))
126.0ms
(/ (* (* (- (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)))))
120.0ms
(fma (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.3b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite181.0ms

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
78.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
63.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
20.0ms
(+ (sqrt (+ x 1)) (sqrt x))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
174.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
156.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms
(* (sqrt x) (sqrt (+ x 1)))
46.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify5.4s

Counts
109 → 150
Calls
109 calls:
Slowest
282.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
279.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
261.0ms
(/ (* (* 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)))))
256.0ms
(/ (* (* 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)))))
238.0ms
(* (* (* (* (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))))

prune845.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1))
0.1b
(* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x))
0.1b
(fma (sqrt x) (sqrt (+ x 1)) x)
0.0b
(sqrt (+ x 1))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×*-un-lft-identity
22×add-exp-log
18×add-cube-cbrt
15×times-frac
9×sqrt-prod
8×add-cbrt-cube div-exp
7×pow1 associate-*l*
6×pow-exp
5×associate-/r*
4×expm1-log1p-u rec-exp unpow-prod-down sqrt-div 1-exp prod-exp insert-posit16 log1p-expm1-u add-log-exp sqr-pow
3×pow-to-exp associate-*r* fma-udef associate-/l*
2×flip3-+ associate-*l/ flip-+ hypot-def distribute-lft-out unswap-sqr
1×distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative cbrt-unprod div-inv pow-flip inv-pow
Counts
4 → 113
Calls
4 calls:
Slowest
14.0ms
(* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x))
9.0ms
(/ 1 (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1))
4.0ms
(sqrt (+ x 1))
0.0ms
(fma (sqrt x) (sqrt (+ x 1)) x)

series413.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ 1 (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1))
151.0ms
(* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x))
72.0ms
(fma (sqrt x) (sqrt (+ x 1)) x)
22.0ms
(sqrt (+ x 1))

simplify10.0s

Counts
89 → 125
Calls
89 calls:
Slowest
564.0ms
(* (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))) (* (* (fma (sqrt x) (sqrt (+ x 1)) x) (fma (sqrt x) (sqrt (+ x 1)) x)) (fma (sqrt x) (sqrt (+ x 1)) x)))
504.0ms
(/ (* (cbrt 1) (cbrt 1)) (* (cbrt (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1)) (cbrt (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1))))
429.0ms
(/ (* (* 1 1) 1) (* (* (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1) (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1)) (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1)))
425.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1)))
258.0ms
(/ (sqrt 1) (sqrt (pow (* (sqrt (+ x 1)) (fma (sqrt x) (sqrt (+ x 1)) x)) 1)))

prune755.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes36.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch1.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
606.0ms1104×body1280valid
568.0ms1917×body640valid
503.0ms7816×body80nan
332.0ms4079×body80valid
107.0ms604×body320valid
35.0ms296×body160valid