Details

Time bar (total: 58.2s)

sample99.0ms

Algorithm
intervals
Results
24.0ms59×body640valid
23.0ms271×body80nan
16.0ms32×body1280valid
15.0ms142×body80valid
4.0ms14×body320valid
2.0ms9×body160valid

simplify38.0ms

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: 17.7b

localize54.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
113×add-sqr-sqrt
97×*-un-lft-identity times-frac
64×sqrt-prod
42×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
12×add-exp-log
9×pow1
8×add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l* add-log-exp
4×sqrt-div div-exp insert-posit16
3×sqrt-pow1 pow1/2
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip--
Calls
4 calls:
Slowest
45.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
17.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
8.0ms
(sqrt (+ x 1))

series189.0ms

Calls
4 calls:
Slowest
82.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
44.0ms
(/ 1 (sqrt (+ x 1)))
33.0ms
(sqrt (+ x 1))
31.0ms
(/ 1 (sqrt x))

simplify4.0s

Calls
204 calls:
Slowest
135.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
109.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
106.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
96.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
64.0ms
(sqrt (+ (pow x 3) (pow 1 3)))

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.2b

localize27.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (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))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
39×sqrt-prod
36×*-un-lft-identity
12×difference-of-squares
11×add-cbrt-cube add-exp-log add-cube-cbrt
10×times-frac associate-/l*
9×pow1 distribute-lft-out--
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
5×distribute-lft-out
4×associate-*r/ insert-posit16 unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Calls
4 calls:
Slowest
108.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
30.0ms
(* (sqrt x) (sqrt (+ x 1)))
28.0ms
(- (sqrt (+ x 1)) (sqrt x))
4.0ms
(sqrt (+ x 1))

series351.0ms

Calls
4 calls:
Slowest
177.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
72.0ms
(- (sqrt (+ x 1)) (sqrt x))
61.0ms
(* (sqrt x) (sqrt (+ x 1)))
40.0ms
(sqrt (+ x 1))

simplify3.2s

Calls
101 calls:
Slowest
375.0ms
(sqrt (* (cbrt (+ x 1)) (cbrt (+ x 1))))
372.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
226.0ms
(/ (* (* (- (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)))))
186.0ms
(- (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))
183.0ms
(/ (* (* (- (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)))))

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 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))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
27×*-un-lft-identity
20×add-cbrt-cube
19×add-sqr-sqrt pow1 sqrt-prod
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×associate-*r* prod-exp
11×add-cube-cbrt
9×pow-prod-down distribute-lft-out
8×frac-times associate-/r/
7×associate-*l* cbrt-unprod
6×div-exp add-log-exp
4×associate-*l/ insert-posit16 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
Calls
4 calls:
Slowest
122.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
65.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
18.0ms
(+ (sqrt (+ x 1)) (sqrt x))
15.0ms
(* (sqrt x) (sqrt (+ x 1)))

series644.0ms

Calls
4 calls:
Slowest
245.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x)))
231.0ms
(/ 1 (* (* (sqrt x) (sqrt (+ x 1))) (+ (sqrt (+ x 1)) (sqrt x))))
93.0ms
(* (sqrt x) (sqrt (+ x 1)))
75.0ms
(+ (sqrt (+ x 1)) (sqrt x))

simplify7.6s

Calls
103 calls:
Slowest
434.0ms
(/ (* (* 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)))))
431.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
372.0ms
(/ (* (* 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)))))
359.0ms
(/ (* (* 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)))))
349.0ms
(* (sqrt (+ (* x x) (- (* 1 1) (* x 1)))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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)))

rewrite165.0ms

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×rec-exp 1-exp insert-posit16 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/
Calls
4 calls:
Slowest
98.0ms
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
25.0ms
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
14.0ms
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
13.0ms
(/ 1 (sqrt (+ x 1)))

series441.0ms

Calls
4 calls:
Slowest
235.0ms
(* (/ (/ 1 (sqrt (+ x 1))) (sqrt x)) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
91.0ms
(/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x)))
81.0ms
(/ (/ 1 (sqrt (+ x 1))) (sqrt x))
35.0ms
(/ 1 (sqrt (+ x 1)))

simplify30.4s

Calls
835 calls:
Slowest
570.0ms
(* (* (* (/ (/ 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)))))
412.0ms
(* (/ (/ 1 (sqrt (sqrt (+ x 1)))) (sqrt (sqrt x))) (/ (sqrt (cbrt 1)) (sqrt (+ (sqrt (+ x 1)) (sqrt x)))))
317.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (cbrt (sqrt x)) (cbrt (sqrt x))))
280.0ms
(/ 1 (* (* (+ (sqrt (+ x 1)) (sqrt x)) (+ (sqrt (+ x 1)) (sqrt x))) (+ (sqrt (+ x 1)) (sqrt x))))
252.0ms
(/ (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (sqrt (+ x 1))) (cbrt (sqrt (+ x 1))))) (* (cbrt (sqrt x)) (cbrt (sqrt x))))

prune4.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes41.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample2.2s

Algorithm
intervals
Results
495.0ms1907×body640valid
470.0ms8072×body80nan
418.0ms628×body320valid
333.0ms1116×body1280valid
309.0ms4028×body80valid
35.0ms321×body160valid