Details

Time bar (total: 2.4m)

sample123.0ms

Algorithm
intervals
Results
33.0ms66×body640valid
29.0ms285×body80nan
19.0ms31×body1280valid
15.0ms125×body80valid
8.0ms22×body320valid
3.0ms12×body160valid

simplify34.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize34.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 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
57.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
16.0ms
(/ 1 (sqrt (+ x 1)))
11.0ms
(sqrt (+ x 1))
10.0ms
(/ 1 (sqrt x))

series211.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
49.0ms
(/ 1 (sqrt x))
32.0ms
(sqrt (+ x 1))
29.0ms
(/ 1 (sqrt (+ x 1)))

simplify1.9m

Counts
1414 → 805
Calls
1414 calls:
Slowest
496.0ms
(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)))))))
412.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (sqrt (* (cbrt x) (cbrt x)))) (/ (cbrt 1) (sqrt (cbrt x))) (- (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))))))
397.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt x)) (cbrt (sqrt x)))) (/ (cbrt 1) (cbrt (sqrt x))) (- (* (/ (cbrt 1) (cbrt (sqrt (+ x 1)))) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))))))
374.0ms
(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)))))))
370.0ms
(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))))))))

prune4.4s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 21.4b

localize14.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
0.0b
(sqrt (+ x 1))

rewrite108.0ms

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))

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
53.0ms
(* (sqrt x) (sqrt (+ x 1)))
52.0ms
(- (sqrt (+ x 1)) (sqrt x))
22.0ms
(sqrt (+ x 1))

simplify5.4s

Counts
193 → 183
Calls
193 calls:
Slowest
346.0ms
(fma (sqrt 1) (sqrt (+ x 1)) (- (* (cbrt (sqrt x)) (* (cbrt (sqrt x)) (cbrt (sqrt x))))))
181.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
163.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
127.0ms
(/ (* (* (- (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)))))
125.0ms
(/ (* (* (- (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)))))

prune987.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))

rewrite179.0ms

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
80.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
62.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms
(+ (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (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))))
155.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
49.0ms
(* (sqrt x) (sqrt (+ x 1)))
47.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify5.5s

Counts
109 → 150
Calls
109 calls:
Slowest
283.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
280.0ms
(* (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)))))
255.0ms
(/ (* (* 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))))

prune854.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
78×times-frac
59×sqrt-prod
46×distribute-lft-out
44×add-sqr-sqrt
36×add-exp-log add-cube-cbrt
20×add-cbrt-cube
18×sqrt-div associate-*r/ associate-/r/
15×div-exp
13×pow1
12×associate-/l*
11×flip3-+ flip-+
9×div-inv
7×cbrt-undiv associate-/r* fma-def associate-*r* prod-exp
6×associate-*l* pow-prod-down add-log-exp
4×expm1-log1p-u rec-exp sqrt-pow1 pow1/2 1-exp insert-posit16 log1p-expm1-u pow-flip unswap-sqr
3×cbrt-unprod
2×clear-num frac-2neg
1×+-commutative sum-log sqrt-unprod *-commutative inv-pow associate-/l/
Counts
4 → 190
Calls
4 calls:
Slowest
42.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms
(+ (sqrt (+ x 1)) (sqrt x))
16.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))

series332.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
176.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (+ (sqrt (+ x 1)) (sqrt x)))
56.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
53.0ms
(* (sqrt x) (sqrt (+ x 1)))
47.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify7.2s

Counts
207 → 202
Calls
207 calls:
Slowest
190.0ms
(/ (/ 1 (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3))))) (* (cbrt (+ (sqrt (+ x 1)) (sqrt x))) (cbrt (+ (sqrt (+ x 1)) (sqrt x)))))
183.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
178.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1)))))
169.0ms
(/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1)))))
161.0ms
(/ (* (* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (/ 1 (* (sqrt x) (sqrt (+ x 1))))) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
609.0ms1069×body1280valid
576.0ms1889×body640valid
475.0ms7851×body80nan
345.0ms4118×body80valid
110.0ms637×body320valid
33.0ms287×body160valid