Details

Time bar (total: 19.3s)

sample77.0ms

Algorithm
intervals
Results
17.0ms57×body640valid
17.0ms249×body80nan
15.0ms37×body1280valid
11.0ms138×body80valid
3.0ms12×body320valid
2.0ms12×body160valid

simplify48.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize17.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))
0.0b
(sqrt (+ x 1))

rewrite86.0ms

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
40.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
17.0ms
(/ 1 (sqrt (+ x 1)))
14.0ms
(sqrt (+ x 1))
10.0ms
(/ 1 (sqrt x))

series206.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
84.0ms
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
52.0ms
(/ 1 (sqrt x))
43.0ms
(/ 1 (sqrt (+ x 1)))
26.0ms
(sqrt (+ x 1))

simplify907.0ms

Counts
179 → 179

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

localize70.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (* (/ 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)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
296×times-frac
274×*-un-lft-identity
209×add-sqr-sqrt
134×sqrt-prod
127×add-cube-cbrt
80×distribute-lft-out
50×add-exp-log
32×frac-sub
30×swap-sqr
29×pow1
28×div-inv
27×pow-flip
25×unswap-sqr
22×associate-/r* associate-*r* associate-*l*
20×add-cbrt-cube
19×div-exp
18×difference-of-squares associate-/l/
17×frac-times associate-*l/ associate-*r/ un-div-inv
16×prod-exp
9×rec-exp sqrt-pow1 pow1/2 1-exp pow-prod-up inv-pow
7×associate-/l*
6×cbrt-undiv add-log-exp
5×pow-prod-down pow-sqr
4×cbrt-unprod insert-posit16
3×associate-/r/
2×clear-num frac-2neg flip3-- flip--
1×pow2 sub-neg flip3-+ pow-plus diff-log div-sub frac-add *-commutative flip-+
Counts
4 → 348
Calls
4 calls:
Slowest
103.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
37.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))
28.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
10.0ms
(/ 1 (sqrt x))

series288.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
168.0ms
(/ (- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1))))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
45.0ms
(- (* (/ 1 (sqrt x)) (/ 1 (sqrt x))) (* (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt (+ x 1)))))
43.0ms
(/ 1 (sqrt x))
31.0ms
(* (/ 1 (sqrt x)) (/ 1 (sqrt x)))

simplify1.8s

Counts
360 → 360

prune3.9s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.3b

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (+ x 1) x)
0.3b
(/ (/ (- (+ x 1) x) (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
0.2b
(/ 1 (sqrt x))
0.1b
(/ 1 (sqrt (+ x 1)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
583×*-un-lft-identity
567×times-frac
230×distribute-lft-out
196×add-sqr-sqrt
184×sqrt-prod
160×add-cube-cbrt
72×div-inv
39×associate-/r/
36×distribute-lft-out--
34×associate-*r/
29×associate-/r*
21×add-exp-log
19×flip3-+ flip-+
18×associate-/l* difference-of-squares
17×add-cbrt-cube
9×div-exp add-log-exp
8×pow1
7×cbrt-undiv
6×pow-flip
4×insert-posit16
3×clear-num frac-2neg
2×rec-exp sqrt-pow1 pow1/2 sqrt-div diff-log 1-exp div-sub inv-pow
1×sum-log sub-neg flip3-- frac-add prod-exp associate--l+ cbrt-unprod flip-- associate-/l/
Counts
4 → 358
Calls
4 calls:
Slowest
121.0ms
(/ (/ (- (+ x 1) x) (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
27.0ms
(- (+ x 1) x)
17.0ms
(/ 1 (sqrt (+ x 1)))
9.0ms
(/ 1 (sqrt x))

series298.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
189.0ms
(/ (/ (- (+ x 1) x) (* x (+ x 1))) (+ (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))
55.0ms
(/ 1 (sqrt x))
52.0ms
(/ 1 (sqrt (+ x 1)))
2.0ms
(- (+ x 1) x)

simplify1.4s

Counts
370 → 370

prune2.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 5.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.7b
(- (+ x 1) x)
0.3b
(* (+ (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt x))) x)
0.2b
(/ 1 (sqrt x))
0.1b
(/ (- (+ x 1) x) (* (* (+ (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt x))) x) (+ x 1)))

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
42×times-frac
37×add-sqr-sqrt
29×add-cube-cbrt
24×sqrt-prod
19×add-exp-log distribute-lft-out
17×add-cbrt-cube
16×associate-*l*
15×associate-*l/
11×associate-/r/
9×associate-/l* add-log-exp
8×pow1 flip3-+ flip-+
7×associate-/r*
6×frac-times div-inv distribute-lft-out--
5×div-exp
4×cbrt-undiv frac-add prod-exp cbrt-unprod insert-posit16
3×associate-*r* pow-flip difference-of-squares
2×clear-num frac-2neg flip3-- diff-log associate-*r/ flip-- associate-/l/
1×rec-exp sum-log sub-neg sqrt-pow1 pow1/2 1-exp div-sub pow-prod-down associate--l+ *-commutative inv-pow unswap-sqr
Counts
4 → 143
Calls
4 calls:
Slowest
120.0ms
(/ (- (+ x 1) x) (* (* (+ (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt x))) x) (+ x 1)))
82.0ms
(* (+ (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt x))) x)
23.0ms
(- (+ x 1) x)
6.0ms
(/ 1 (sqrt x))

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
151.0ms
(/ (- (+ x 1) x) (* (* (+ (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt x))) x) (+ x 1)))
92.0ms
(* (+ (/ 1 (sqrt (+ x 1))) (/ 1 (sqrt x))) x)
30.0ms
(/ 1 (sqrt x))
1.0ms
(- (+ x 1) x)

simplify818.0ms

Counts
155 → 155

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes37.0ms

Accuracy

0% (0.3b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch2.0ms

end0.0ms

sample2.9s

Algorithm
intervals
Results
660.0ms7752×body80nan
627.0ms1871×body640valid
507.0ms1128×body1280valid
404.0ms4077×body80valid
361.0ms307×body160valid
147.0ms617×body320valid