Details

Time bar (total: 12.9s)

sample43.0ms

Algorithm
intervals
Results
8.0ms56×body640valid
7.0ms250×body80nan
5.0ms142×body80valid
5.0ms29×body1280valid
2.0ms17×body320valid
1.0ms12×body160valid

simplify12.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
11111
21411
done1411

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
3.2b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
75×*-un-lft-identity
73×add-sqr-sqrt
69×times-frac
50×sqrt-prod
42×add-cube-cbrt
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv frac-2neg flip3-+ div-exp clear-num associate-/r/ flip-+
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
15.0ms
(sqrt (+ x 1.0))
31.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
107.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(sqrt (+ x 1.0))
94.0ms
(/ 1.0 (sqrt (+ x 1.0)))
55.0ms
(/ 1.0 (sqrt x))
212.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify908.0ms

Counts
145 → 145
Iterations

Useful iterations: done (901.0ms)

IterNodesCost
02151942
14631778
216801704
done50011700

prune486.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 17.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
3.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite199.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-exp-log add-cbrt-cube
9×pow1 add-cube-cbrt
7×associate-*r*
6×sqrt-div associate-*r/ associate-*l* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp difference-of-squares unswap-sqr
3×sqrt-pow1 flip3-+ pow1/2 pow-prod-down flip-+ distribute-lft-out distribute-lft-out--
2×flip3-- associate-/r/ flip-- associate-/l/
1×sub-neg rem-sqrt-square frac-2neg times-frac sqrt-unprod diff-log clear-num associate-/r* *-commutative div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
90.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
38.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
60.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series576.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(sqrt (+ x 1.0))
359.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
87.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
91.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.7s

Counts
105 → 105
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01891624
15341471
230701232
done50011218

prune416.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 16.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))
0.2b
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.7b
(- (+ x 1.0) x)

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
113×*-un-lft-identity
46×add-sqr-sqrt
39×sqrt-prod
37×times-frac distribute-lft-out
29×add-exp-log add-cbrt-cube
22×add-cube-cbrt
16×distribute-lft-out--
9×cbrt-undiv div-exp add-log-exp
8×pow1 prod-exp cbrt-unprod difference-of-squares
7×associate-*r* associate-/r* associate-/l*
6×associate-*l*
5×associate-*r/
4×sqrt-div associate-/r/ unswap-sqr
3×flip3-+ pow-prod-down flip-+ associate-/l/
2×flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log clear-num flip-- div-inv
1×sub-neg sqrt-unprod div-sub associate--l+ sum-log *-commutative
Counts
4 → 143
Calls
4 calls:
128.0ms
(/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))
107.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
29.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
42.0ms
(- (+ x 1.0) x)

series1.0s

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))
721.0ms
(/ (* 1.0 (/ (- (+ x 1.0) x) (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
80.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms
(- (+ x 1.0) x)

simplify480.0ms

Counts
155 → 155
Iterations

Useful iterations: done (474.0ms)

IterNodesCost
02703162
17962943
done50002554

prune485.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
0.2b
(/ (* 1.0 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
31×sqrt-prod
29×add-exp-log add-sqr-sqrt add-cbrt-cube
20×add-cube-cbrt
19×times-frac
18×distribute-lft-out
9×pow1 cbrt-undiv div-exp
8×prod-exp cbrt-unprod
7×associate-*r* associate-/r*
6×sqrt-div associate-*l*
5×associate-*r/
4×flip3-+ associate-/r/ flip-+ associate-/l* add-log-exp unswap-sqr
3×sqrt-pow1 pow1/2 pow-prod-down
2×frac-2neg clear-num div-inv
1×rem-sqrt-square sqrt-unprod *-commutative associate-/l/
Counts
4 → 118
Calls
4 calls:
14.0ms
(sqrt (+ x 1.0))
51.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
47.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
38.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (+ x 1.0))
180.0ms
(/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))
775.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
101.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify2.2s

Counts
130 → 130
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02492257
17092046
245921729
done50001717

prune300.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01018
11418
done1418

end0.0ms

sample1.8s

Algorithm
intervals
Results
533.0ms1184×body1280valid
374.0ms1809×body640valid
309.0ms7835×body80nan
182.0ms4100×body80valid
94.0ms627×body320valid
18.0ms280×body160valid