Details

Time bar (total: 12.9s)

sample74.0ms

Algorithm
intervals
Results
15.0ms63×body640valid
13.0ms255×body80nan
11.0ms34×body1280valid
9.0ms134×body80valid
2.0ms13×body320valid
2.0ms12×body160valid

simplify26.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize19.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
2.9b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite151.0ms

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:
15.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
121.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series378.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ 1.0 (sqrt (+ x 1.0)))
78.0ms
(/ 1.0 (sqrt x))
177.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify637.0ms

Counts
126 → 126

prune478.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 19.4b

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.9b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite198.0ms

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:
114.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
53.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series558.0ms

Counts
3 → 9
Calls
3 calls:
387.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
76.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
95.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.1s

Counts
86 → 86

prune351.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 18.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* 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)))
2.4b
(+ x (- 1.0 x))

rewrite286.0ms

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:
130.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
60.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
52.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
31.0ms
(+ x (- 1.0 x))

series1.0s

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
724.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
70.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
2.0ms
(+ x (- 1.0 x))

simplify1.4s

Counts
148 → 148

prune468.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

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)))

rewrite186.0ms

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:
40.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
56.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
31.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
84.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
179.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
964.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
69.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify1.3s

Counts
128 → 128

prune368.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes84.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify612.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
573.0ms7985×body80nan
333.0ms1128×body1280valid
278.0ms1863×body640valid
213.0ms4118×body80valid
100.0ms608×body320valid
18.0ms283×body160valid