Details

Time bar (total: 30.4s)

sample92.0ms

Algorithm
intervals
Results
19.0ms278×body80nan
18.0ms56×body640valid
15.0ms20×body320valid
15.0ms33×body1280valid
12.0ms142×body80valid
1.0ms5×body160valid

simplify37.0ms

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize14.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
11×add-sqr-sqrt
9×associate-/r*
8×add-cube-cbrt
6×pow1 add-exp-log sqrt-prod div-inv add-log-exp
4×add-cbrt-cube sqrt-div insert-posit16 pow-flip distribute-lft-out--
3×pow1/2
2×rec-exp clear-num frac-2neg flip3-+ associate-/r/ flip-+ inv-pow
1×rem-sqrt-square sub-neg flip3-- diff-log frac-sub flip-- difference-of-squares
Calls
4 calls:
Slowest
7.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
3.0ms
(/ 1 (sqrt (+ x 1)))
1.0ms
(sqrt (+ x 1))
1.0ms
(/ 1 (sqrt x))

series97.0ms

Calls
4 calls:
Slowest
57.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
18.0ms
(/ 1 (sqrt x))
12.0ms
(/ 1 (sqrt (+ x 1)))
11.0ms
(sqrt (+ x 1))

simplify803.0ms

Calls
42 calls:
Slowest
133.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
90.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
89.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
41.0ms
(/ (exp (/ 1 (sqrt x))) (exp (/ 1 (sqrt (+ x 1)))))
40.0ms
(sqrt (- (* x x) (* 1 1)))

prune783.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 17.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.4b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1 (sqrt x))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×frac-sub
14×add-exp-log pow-flip
9×frac-times associate-*l/ associate-*r/ un-div-inv
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt inv-pow
6×rec-exp associate-/r* add-cbrt-cube pow1/2 pow-prod-up add-log-exp
4×associate-*r* associate-*l* pow-prod-down prod-exp insert-posit16 div-inv
2×clear-num frac-2neg
1×pow2 sub-neg pow-plus flip3-- diff-log *-commutative cbrt-unprod flip-- difference-of-squares
Calls
4 calls:
Slowest
8.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
5.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
1.0ms
(/ 1 (sqrt x))
1.0ms
(/ 1 (sqrt x))

series58.0ms

Calls
4 calls:
Slowest
25.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
12.0ms
(/ 1 (sqrt x))
11.0ms
(/ 1 (sqrt x))
10.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify3.7s

Calls
91 calls:
Slowest
248.0ms
(/ (exp (* (/ 1 (sqrt x)) (/ 1 (sqrt x)))) (exp (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))))
208.0ms
(- (* (* (/ 1 (sqrt x)) 1) (sqrt (+ x 1))) (* (sqrt x) (/ 1 (sqrt (+ x 1)))))
180.0ms
(- (* (/ 1 (sqrt x)) (sqrt (+ x 1))) (* (sqrt x) (* (/ 1 (sqrt (+ x 1))) 1)))
179.0ms
(- (* (* 1 (/ 1 (sqrt x))) (sqrt (+ x 1))) (* (sqrt x) (* 1 (/ 1 (sqrt (+ x 1))))))
177.0ms
(- (* (* 1 (/ 1 (sqrt x))) (* (sqrt (+ x 1)) (sqrt (+ x 1)))) (* (sqrt x) (* 1 1)))

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.6b

localize16.0ms

Local error

Found 4 expressions with local error:

5.8b
(/ (/ 1 (+ (* x x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.3b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (+ (* x x) x))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
51×*-un-lft-identity
42×times-frac
40×div-inv
28×distribute-lft-out
23×add-sqr-sqrt associate-/r/ add-cube-cbrt
20×associate-/r*
11×flip3-+ add-exp-log flip-+
7×pow1
6×add-cbrt-cube associate-/l*
5×pow-flip
4×rec-exp clear-num frac-2neg insert-posit16 add-log-exp
3×sqrt-prod inv-pow
2×pow1/2 sqrt-div div-exp
1×cbrt-undiv distribute-lft1-in frac-add associate-/l/
Calls
4 calls:
Slowest
11.0ms
(/ (/ 1 (+ (* x x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
2.0ms
(/ 1 (+ (* x x) x))
1.0ms
(/ 1 (sqrt (+ x 1)))
1.0ms
(/ 1 (sqrt x))

series120.0ms

Calls
4 calls:
Slowest
81.0ms
(/ (/ 1 (+ (* x x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
15.0ms
(/ 1 (sqrt x))
13.0ms
(/ 1 (sqrt (+ x 1)))
11.0ms
(/ 1 (+ (* x x) x))

simplify14.3s

Calls
134 calls:
Slowest
479.0ms
(/ (+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
476.0ms
(/ (+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
475.0ms
(/ (+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
451.0ms
(/ (+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
426.0ms
(/ (+ (* (* x x) (* x x)) (- (* x x) (* (* x x) x))) (sqrt (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))))

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
15×flip3-+ flip-+
13×associate-/r/
12×frac-times
11×*-un-lft-identity
10×associate-/r*
9×add-sqr-sqrt pow1 add-exp-log add-cube-cbrt
6×add-cbrt-cube associate-*l/ frac-add
5×associate-*l* div-inv
4×associate-*r/ insert-posit16 add-log-exp
3×clear-num frac-2neg associate-*r* sqrt-prod
2×rec-exp sqrt-div pow-prod-down prod-exp pow-flip distribute-lft-out
1×distribute-rgt-in distribute-lft-in *-commutative cbrt-unprod inv-pow
Calls
4 calls:
Slowest
13.0ms
(* (+ (/ x (sqrt (+ x 1))) (/ x (sqrt x))) (+ x 1))
8.0ms
(/ 1 (* (+ (/ x (sqrt (+ x 1))) (/ x (sqrt x))) (+ x 1)))
1.0ms
(/ x (sqrt (+ x 1)))
0.0ms
(/ x (sqrt x))

series139.0ms

Calls
4 calls:
Slowest
58.0ms
(/ 1 (* (+ (/ x (sqrt (+ x 1))) (/ x (sqrt x))) (+ x 1)))
44.0ms
(* (+ (/ x (sqrt (+ x 1))) (/ x (sqrt x))) (+ x 1))
20.0ms
(/ x (sqrt (+ x 1)))
17.0ms
(/ x (sqrt x))

simplify4.7s

Calls
64 calls:
Slowest
407.0ms
(* (+ (pow (/ x (sqrt (+ x 1))) 3) (pow (/ x (sqrt x)) 3)) (+ (pow x 3) (pow 1 3)))
344.0ms
(* (- (* (/ x (sqrt (+ x 1))) (/ x (sqrt (+ x 1)))) (* (/ x (sqrt x)) (/ x (sqrt x)))) (+ (pow x 3) (pow 1 3)))
218.0ms
(* (* (sqrt (+ x 1)) (sqrt x)) (+ (* x x) (- (* 1 1) (* x 1))))
217.0ms
(* (+ (* x (sqrt x)) (* (sqrt (+ x 1)) x)) (- (* x x) (* 1 1)))
217.0ms
(* (+ (pow (/ x (sqrt (+ x 1))) 3) (pow (/ x (sqrt x)) 3)) (+ x 1))

prune619.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes30.0ms

Accuracy

0% (0.3b remaining)

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

bsearch3.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
548.0ms4121×body80valid
497.0ms8167×body80nan
486.0ms1796×body640valid
398.0ms1180×body1280valid
167.0ms621×body320valid
31.0ms282×body160valid