Details

Time bar (total: 2.1m)

sample119.0ms

Algorithm
intervals
Results
32.0ms67×body640valid
26.0ms274×body80nan
18.0ms31×body1280valid
15.0ms128×body80valid
7.0ms21×body320valid
2.0ms9×body160valid

simplify462.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
462.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize17.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
110×add-sqr-sqrt
97×times-frac
93×*-un-lft-identity
60×sqrt-prod
40×add-cube-cbrt
25×difference-of-squares
13×associate-/r* distribute-lft-out--
11×add-exp-log
7×pow1 add-cbrt-cube distribute-lft-out
6×div-inv pow-flip associate-/l*
5×add-log-exp
4×div-exp
3×insert-posit16
2×cbrt-undiv rec-exp clear-num frac-2neg sqrt-pow1 pow1/2 sqrt-div 1-exp associate-/r/ inv-pow
1×sub-neg flip3-+ flip3-- diff-log frac-sub flip-+ flip--
Counts
3 → 150
Calls
3 calls:
Slowest
22.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
9.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series155.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
76.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
45.0ms
(/ 1 (sqrt (+ x 1)))
33.0ms
(/ 1 (sqrt x))

simplify6.7s

Counts
226 → 159
Calls
226 calls:
Slowest
636.0ms
(* (* (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))) (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
511.0ms
(- (pow (/ 1 (sqrt x)) 3) (pow (/ 1 (sqrt (+ x 1))) 3))
302.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
178.0ms
(/ 1 (sqrt (+ (pow x 3) (pow 1 3))))
155.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 20.5b

localize31.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (sqrt (+ x 1)) (sqrt x))
0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.1b
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×sqrt-prod
32×*-un-lft-identity
12×difference-of-squares
10×times-frac add-cbrt-cube add-exp-log associate-/l*
9×add-cube-cbrt distribute-lft-out--
7×pow1 associate-*r*
6×associate-*l*
5×add-log-exp
4×sqrt-div associate-*r/ distribute-lft-out unswap-sqr
3×pow-prod-down insert-posit16
2×cbrt-undiv sqrt-pow1 flip3-+ flip3-- pow1/2 div-exp prod-exp associate-/r/ cbrt-unprod flip-+ flip-- associate-/l/
1×clear-num associate-/r* sub-neg frac-2neg sqrt-unprod diff-log div-sub *-commutative div-inv
Counts
3 → 95
Calls
3 calls:
Slowest
76.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
55.0ms
(- (sqrt (+ x 1)) (sqrt x))
31.0ms
(* (sqrt x) (sqrt (+ x 1)))

series365.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
212.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ x 1))))
89.0ms
(* (sqrt x) (sqrt (+ x 1)))
64.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify6.5s

Counts
125 → 104
Calls
125 calls:
Slowest
356.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
352.0ms
(* (* (* (sqrt x) (sqrt (+ x 1))) (* (sqrt x) (sqrt (+ x 1)))) (* (sqrt x) (sqrt (+ x 1))))
319.0ms
(* (* (- (sqrt (+ x 1)) (sqrt x)) (- (sqrt (+ x 1)) (sqrt x))) (- (sqrt (+ x 1)) (sqrt x)))
278.0ms
(* (* (sqrt x) (sqrt (+ x 1))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (+ (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
272.0ms
(/ (- (sqrt (+ x 1)) (sqrt x)) (* (sqrt x) (sqrt (+ (pow x 3) (pow 1 3)))))

prune971.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
110×*-un-lft-identity
78×times-frac
51×sqrt-prod
46×add-sqr-sqrt
41×distribute-lft-out
38×add-cube-cbrt
31×add-exp-log
27×associate-/l*
19×add-cbrt-cube
14×div-exp
8×pow1 associate-/r/
7×cbrt-undiv associate-/r* associate-*r*
6×associate-*l*
5×flip3-+ prod-exp flip-+
4×sqrt-div associate-*r/ div-inv unswap-sqr
3×rec-exp 1-exp pow-prod-down cbrt-unprod insert-posit16 add-log-exp
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×sqrt-unprod *-commutative pow-flip inv-pow associate-/l/
Counts
3 → 155
Calls
3 calls:
Slowest
66.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
25.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
19.0ms
(* (sqrt x) (sqrt (+ x 1)))

series445.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
257.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1))))
97.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
90.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify15.9s

Counts
210 → 164
Calls
210 calls:
Slowest
500.0ms
(* (* (* (sqrt x) (sqrt x)) (sqrt x)) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
380.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (+ (* (sqrt (+ x 1)) (sqrt (+ x 1))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1)) (sqrt x)))))
376.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (/ (cbrt 1) (+ (sqrt (+ x 1)) (sqrt x))))
366.0ms
(/ (/ 1 (- (* (sqrt (+ x 1)) (sqrt (+ x 1))) (* (sqrt x) (sqrt x)))) (sqrt x))
360.0ms
(/ (* (sqrt x) (sqrt (+ x 1))) (/ (sqrt 1) (+ (sqrt (+ x 1)) (sqrt x))))

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1)))
0.2b
(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
2754×times-frac
2239×sqrt-prod
2068×*-un-lft-identity
765×distribute-lft-out
737×add-sqr-sqrt
729×add-cube-cbrt
155×associate-/r/
92×div-inv
64×flip3-+ flip-+
44×associate-/r*
33×associate-/l*
31×sqrt-div
23×add-exp-log
19×add-cbrt-cube
10×pow1
9×div-exp
7×cbrt-undiv associate-*r*
6×associate-*l*
4×insert-posit16 add-log-exp unswap-sqr
3×clear-num frac-2neg pow-prod-down
2×rec-exp sqrt-undiv sqrt-pow1 pow1/2 sqrt-unprod 1-exp prod-exp associate-*r/ cbrt-unprod pow-flip inv-pow
1×*-commutative associate-/l/
Counts
4 → 1069
Calls
4 calls:
Slowest
98.0ms
(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
28.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
25.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
16.0ms
(* (sqrt x) (sqrt (+ x 1)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
199.0ms
(/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))
75.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
74.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))
70.0ms
(* (sqrt x) (sqrt (+ x 1)))

simplify1.3m

Counts
1985 → 1081
Calls
1985 calls:
Slowest
581.0ms
(* (* (/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))) (/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))))) (/ (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (/ (* (sqrt x) (sqrt (+ x 1))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))))
426.0ms
(- (log (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (- (log (* (sqrt x) (sqrt (+ x 1)))) (log (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))))
298.0ms
(/ (/ 1 (+ (sqrt (+ x 1)) (sqrt x))) (/ (* x (+ x 1)) (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
286.0ms
(/ (sqrt (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x))))) (/ (sqrt x) (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))))
284.0ms
(/ (sqrt (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x))))) (/ (sqrt x) (sqrt (/ 1 (+ (pow (sqrt (+ x 1)) 3) (pow (sqrt x) 3))))))

prune7.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.5b remaining)

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

bsearch3.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
517.0ms1796×body640valid
503.0ms4178×body80valid
463.0ms8167×body80nan
333.0ms1094×body1280valid
121.0ms636×body320valid
32.0ms296×body160valid