Details

Time bar (total: 14.6s)

sample78.0ms

Algorithm
intervals
Results
19.0ms70×body640valid
15.0ms265×body80nan
9.0ms130×body80valid
8.0ms25×body1280valid
4.0ms23×body320valid
1.0ms8×body160valid

simplify28.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
71×*-un-lft-identity
70×add-sqr-sqrt
69×times-frac
46×sqrt-prod
40×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l*
5×add-log-exp
4×div-inv
3×pow1
2×cbrt-undiv frac-2neg sqrt-div div-exp clear-num associate-/r/
1×sub-neg flip3-- flip3-+ diff-log frac-sub flip-- flip-+
Counts
3 → 117
Calls
3 calls:
17.0ms
(/ 1.0 (sqrt (+ x 1.0)))
13.0ms
(/ 1.0 (sqrt x))
124.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series314.0ms

Counts
3 → 9
Calls
3 calls:
110.0ms
(/ 1.0 (sqrt (+ x 1.0)))
47.0ms
(/ 1.0 (sqrt x))
157.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify699.0ms

Counts
126 → 126

prune458.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 21.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite222.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×sqrt-prod
17×add-exp-log add-cbrt-cube
16×*-un-lft-identity
7×pow1 add-cube-cbrt associate-*r*
6×associate-*r/ associate-*l*
5×prod-exp cbrt-unprod add-log-exp
4×cbrt-undiv sqrt-div div-exp difference-of-squares unswap-sqr
3×pow-prod-down distribute-lft-out--
2×flip3-- sqrt-pow1 flip3-+ pow1/2 associate-/r/ flip-- flip-+ associate-/l/ distribute-lft-out
1×sub-neg frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
3 → 77
Calls
3 calls:
97.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
46.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
74.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series523.0ms

Counts
3 → 9
Calls
3 calls:
365.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
75.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
82.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.1s

Counts
86 → 86

prune415.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
1.9b
(+ x (- 1.0 x))

rewrite323.0ms

Algorithm
rewrite-expression-head
Rules
105×*-un-lft-identity
41×distribute-lft-out
35×sqrt-prod
31×times-frac
29×add-exp-log add-sqr-sqrt add-cbrt-cube
21×add-cube-cbrt
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod distribute-lft-out--
7×associate-*r* associate-/r*
6×associate-*l* associate-/l*
5×flip3-+ associate-*r/ flip-+
4×sqrt-div associate-/r/ unswap-sqr
3×pow-prod-down associate-/l/
2×associate-+r- associate-+r+ frac-2neg sqrt-pow1 pow1/2 clear-num sum-log div-inv
1×+-commutative sub-neg sqrt-unprod diff-log div-sub *-commutative
Counts
4 → 136
Calls
4 calls:
143.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
101.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
56.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
17.0ms
(+ x (- 1.0 x))

series949.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
635.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
92.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(+ x (- 1.0 x))

simplify1.3s

Counts
148 → 148

prune441.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite190.0ms

Algorithm
rewrite-expression-head
Rules
56×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-cbrt-cube
27×add-sqr-sqrt
21×distribute-lft-out
19×add-cube-cbrt times-frac
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×associate-*l* add-log-exp
5×associate-*r/
4×flip3-+ sqrt-div associate-/r/ flip-+ associate-/l* unswap-sqr
3×pow-prod-down
2×frac-2neg sqrt-pow1 pow1/2 clear-num div-inv
1×+-commutative sqrt-unprod sum-log *-commutative associate-/l/
Counts
4 → 116
Calls
4 calls:
47.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
46.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
64.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
28.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.0s

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
183.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
663.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
78.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.2s

Counts
128 → 128

prune388.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes57.0ms

Accuracy

28.6% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.6s

end0.0ms

sample2.0s

Algorithm
intervals
Results
546.0ms1116×body1280valid
487.0ms1851×body640valid
335.0ms8036×body80nan
193.0ms4054×body80valid
113.0ms657×body320valid
25.0ms322×body160valid