Details

Time bar (total: 2.5m)

sample101.0ms

Algorithm
intervals
Results
24.0ms56×body640valid
22.0ms251×body80nan
19.0ms38×body1280valid
15.0ms135×body80valid
5.0ms17×body320valid
2.0ms10×body160valid

simplify51.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
51.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize33.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite142.0ms

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
62.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
17.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
9.0ms
(sqrt (+ x 1))

series263.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
54.0ms
(/ 1 (sqrt (+ x 1)))
47.0ms
(/ 1 (sqrt x))
40.0ms
(sqrt (+ x 1))

simplify1.9m

Counts
1414 → 805
Calls
1414 calls:
Slowest
371.0ms
(fma (- (sqrt (/ 1 (sqrt (+ x 1))))) (sqrt (/ 1 (sqrt (+ x 1)))) (* (sqrt (/ 1 (sqrt (+ x 1)))) (sqrt (/ 1 (sqrt (+ x 1))))))
367.0ms
(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)))))))
365.0ms
(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))))))))
364.0ms
(fma (- (/ 1 (sqrt (cbrt (+ x 1))))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))) (* (/ 1 (sqrt (cbrt (+ x 1)))) (/ 1 (sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1)))))))
344.0ms
(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))))))))

prune4.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.6b

localize17.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (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))))
31.0ms
(- (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))
4.0ms
(sqrt (+ x 1))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
138.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
55.0ms
(- (sqrt (+ x 1)) (sqrt x))
53.0ms
(* (sqrt x) (sqrt (+ x 1)))
26.0ms
(sqrt (+ x 1))

simplify5.5s

Counts
193 → 183
Calls
193 calls:
Slowest
266.0ms
(fma (- (sqrt (sqrt x))) (sqrt (sqrt x)) (* (sqrt (sqrt x)) (sqrt (sqrt x))))
181.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
162.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
129.0ms
(/ (* (* (- (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)))))
127.0ms
(/ (* (* (- (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)))))

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ 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))

rewrite178.0ms

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))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
179.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
158.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
50.0ms
(* (sqrt x) (sqrt (+ x 1)))
49.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify5.6s

Counts
109 → 150
Calls
109 calls:
Slowest
286.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
285.0ms
(* (sqrt (- x 1)) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
263.0ms
(/ (* (* 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)))))
261.0ms
(/ (* (* 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)))))
242.0ms
(* (* (* (* (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))))

prune867.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
104×add-exp-log
85×*-un-lft-identity
48×add-sqr-sqrt
44×times-frac prod-exp
39×sqrt-prod
36×div-exp
34×add-cbrt-cube
33×add-cube-cbrt
31×associate-*r*
29×distribute-lft-out
21×pow1
18×rec-exp 1-exp
15×associate-*l*
11×pow-prod-down
10×cbrt-undiv cbrt-unprod
9×pow-flip
8×associate-/r/
7×associate-/r* associate-*r/ unswap-sqr
6×sqrt-div associate-/l*
5×flip3-+ flip-+
4×expm1-log1p-u sqrt-pow1 pow1/2 insert-posit16 log1p-expm1-u div-inv inv-pow add-log-exp
2×clear-num frac-2neg *-commutative
1×frac-times sqrt-unprod associate-*l/ un-div-inv
Counts
4 → 208
Calls
4 calls:
Slowest
99.0ms
(* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
24.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(* (sqrt x) (sqrt (+ x 1)))
16.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))

series350.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(* (/ 1 (* (sqrt x) (sqrt (+ x 1)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))
63.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
57.0ms
(/ 1 (* (sqrt x) (sqrt (+ x 1))))
53.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify8.6s

Counts
194 → 220
Calls
194 calls:
Slowest
290.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))) (/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
217.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))) (/ (* (* 1 1) 1) (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x)))))
193.0ms
(+ (- (log 1) (+ (log (sqrt x)) (log (sqrt (+ x 1))))) (- 0 (log (+ (sqrt (+ x 1)) (sqrt x)))))
193.0ms
(+ (- 0 (+ (log (sqrt x)) (log (sqrt (+ x 1))))) (- 0 (log (+ (sqrt (+ x 1)) (sqrt x)))))
185.0ms
(* (/ (* (* 1 1) 1) (* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))) (* (* (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch3.0ms

end0.0ms

sample2.5s

Algorithm
intervals
Results
848.0ms1872×body640valid
496.0ms7972×body80nan
428.0ms1136×body1280valid
364.0ms4084×body80valid
137.0ms608×body320valid
38.0ms300×body160valid