Details

Time bar (total: 2.4m)

sample79.0ms

Algorithm
intervals
Results
20.0ms288×body80nan
15.0ms39×body1280valid
14.0ms50×body640valid
11.0ms136×body80valid
5.0ms23×body320valid
1.0ms8×body160valid

simplify52.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
52.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize17.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite77.0ms

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--
Counts
4 → 167
Calls
4 calls:
Slowest
32.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
23.0ms
(/ 1 (sqrt (+ x 1)))
10.0ms
(/ 1 (sqrt x))
8.0ms
(sqrt (+ x 1))

series209.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
90.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
42.0ms
(/ 1 (sqrt (+ x 1)))
42.0ms
(sqrt (+ x 1))
34.0ms
(/ 1 (sqrt x))

simplify4.0s

Counts
204 → 179
Calls
204 calls:
Slowest
164.0ms
(/ (* (* 1 1) 1) (* (* (sqrt (+ x 1)) (sqrt (+ x 1))) (sqrt (+ x 1))))
106.0ms
(- (+ (* 1/2 x) 1) (* 1/8 (pow x 2)))
91.0ms
(- (+ (* 3/8 (pow x 2)) 1) (* 1/2 x))
81.0ms
(sqrt (+ (* x x) (- (* 1 1) (* x 1))))
66.0ms
(/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x)))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 18.1b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
0.5b
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
0.3b
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
426×times-frac
387×*-un-lft-identity
340×add-sqr-sqrt
208×sqrt-prod
176×add-cube-cbrt
98×distribute-lft-out
86×add-exp-log
71×swap-sqr
50×pow1 unswap-sqr
49×associate-*r* associate-*l*
48×pow-flip
33×div-exp div-inv
32×prod-exp frac-sub
30×add-cbrt-cube
18×frac-times associate-*l/ associate-*r/ un-div-inv pow-prod-up difference-of-squares associate-/l/
16×rec-exp associate-/r* sqrt-pow1 pow1/2 1-exp inv-pow
11×associate-/r/
10×pow-prod-down pow-sqr
9×cbrt-undiv
8×sqrt-div cbrt-unprod
6×add-log-exp
5×flip3-+ flip-+
4×insert-posit16 associate-/l*
2×pow2 pow-plus flip3-- *-commutative flip--
1×clear-num sub-neg frac-2neg diff-log div-sub frac-add
Counts
4 → 476
Calls
4 calls:
Slowest
88.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
51.0ms
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))
29.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
27.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
63.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
35.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
15.0ms
(* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))

simplify41.6s

Counts
672 → 488
Calls
672 calls:
Slowest
670.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
635.0ms
(/ (* (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))) (cbrt (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))))) (/ (* (cbrt 1) (cbrt 1)) 1))
598.0ms
(* (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))) (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))))
466.0ms
(* (* (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (/ 1 (sqrt x))) (/ (* (* 1 1) 1) (* (* (sqrt x) (sqrt x)) (sqrt x))))
454.0ms
(* (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))) (* (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))) (/ 1 (sqrt (+ x 1)))))

prune3.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 4.5b

localize25.0ms

Local error

Found 4 expressions with local error:

4.8b
(/ (/ 1 (+ (* x x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.1b
(/ 1 (+ (* x x) x))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
1041×times-frac
965×*-un-lft-identity
356×distribute-lft-out
352×add-sqr-sqrt add-cube-cbrt
292×sqrt-prod
109×div-inv
55×distribute-lft1-in distribute-rgt-out
41×associate-/r/
34×associate-/r*
30×associate-/l*
25×add-exp-log
20×flip3-+ flip-+
15×add-cbrt-cube
12×div-exp
9×pow1
7×pow-flip
6×cbrt-undiv
4×rec-exp clear-num frac-2neg 1-exp insert-posit16 add-log-exp
3×inv-pow
2×sqrt-pow1 pow1/2 sqrt-div
1×frac-add associate-/l/
Counts
4 → 534
Calls
4 calls:
Slowest
52.0ms
(/ (/ 1 (+ (* x x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
11.0ms
(/ 1 (+ (* x x) x))
8.0ms
(/ 1 (sqrt (+ x 1)))
5.0ms
(/ 1 (sqrt x))

series210.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(/ (/ 1 (+ (* x x) x)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
31.0ms
(/ 1 (sqrt x))
28.0ms
(/ 1 (sqrt (+ x 1)))
19.0ms
(/ 1 (+ (* x x) x))

simplify51.6s

Counts
879 → 546
Calls
879 calls:
Slowest
418.0ms
(/ (/ (sqrt 1) (+ x 1)) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
412.0ms
(/ (/ 1 (- (* (* x x) (* x x)) (* x x))) (/ (* (cbrt 1) (cbrt 1)) (sqrt 1)))
313.0ms
(/ (/ 1 (- (* (* x x) (* x x)) (* x x))) (/ 1 1))
302.0ms
(/ (/ 1 (- (* (* x x) (* x x)) (* x x))) (/ (sqrt 1) (sqrt 1)))
299.0ms
(/ (/ 1 (- (* (* x x) (* x x)) (* x x))) (/ (sqrt 1) (sqrt 1)))

prune3.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ x (sqrt x))
0.3b
(/ x (sqrt (+ 1 x)))
0.2b
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
0.0b
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
852×*-un-lft-identity
831×times-frac
329×distribute-lft-out
294×add-sqr-sqrt add-cube-cbrt
268×sqrt-prod
58×div-inv
35×associate-/r/
27×associate-/r*
24×associate-/l*
18×flip3-+ flip-+
17×add-exp-log
13×add-cbrt-cube
8×div-exp
7×pow1
6×add-log-exp
5×cbrt-undiv
4×insert-posit16
3×clear-num frac-2neg
2×sqrt-div frac-add pow-div
1×+-commutative rec-exp sum-log sqrt-pow1 pow1/2 1-exp associate-/l/
Counts
4 → 417
Calls
4 calls:
Slowest
47.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
25.0ms
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))
7.0ms
(/ x (sqrt (+ 1 x)))
4.0ms
(/ x (sqrt x))

series334.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ (/ 1 (+ 1 x)) (+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x))))
91.0ms
(+ (/ x (sqrt (+ 1 x))) (/ x (sqrt x)))
57.0ms
(/ x (sqrt (+ 1 x)))
44.0ms
(/ x (sqrt x))

simplify34.3s

Counts
681 → 429
Calls
681 calls:
Slowest
408.0ms
(/ (* (* x x) x) (* (* (sqrt x) (sqrt x)) (sqrt x)))
348.0ms
(/ (/ (sqrt 1) (+ 1 x)) (+ (/ (sqrt x) (sqrt (+ 1 x))) (/ (sqrt x) (sqrt x))))
324.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) 1))
320.0ms
(/ (/ (sqrt 1) (* (cbrt (+ 1 x)) (cbrt (+ 1 x)))) (/ (* (cbrt x) (cbrt x)) 1))
306.0ms
(/ (/ 1 (+ (pow 1 3) (pow x 3))) (/ (* (cbrt x) (cbrt x)) (sqrt 1)))

prune2.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes28.0ms

Accuracy

0% (0.2b remaining)

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

bsearch2.0ms

end0.0ms

sample2.4s

Algorithm
intervals
Results
815.0ms1865×body640valid
480.0ms8044×body80nan
470.0ms1118×body1280valid
305.0ms4109×body80valid
133.0ms594×body320valid
39.0ms314×body160valid