Details

Time bar (total: 21.8s)

sample69.0ms

Algorithm
intervals
Results
13.0ms270×body80nan
11.0ms49×body640valid
11.0ms36×body1280valid
8.0ms134×body80valid
4.0ms22×body320valid
2.0ms15×body160valid

simplify24.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
4.0b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-cbrt-cube add-exp-log
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub hypot-def flip--
Counts
4 → 758
Calls
4 calls:
6.0ms
(sqrt (+ x 1.0))
9.0ms
(/ 1.0 (sqrt (+ x 1.0)))
5.0ms
(/ 1.0 (sqrt x))
112.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series389.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(sqrt (+ x 1.0))
120.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
192.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.5s

Counts
770 → 770
Iterations
IterNodes
done5000
23579
11587
0702

prune4.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 18.1b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
3.9b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite258.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
240×*-un-lft-identity
167×add-sqr-sqrt
125×add-cube-cbrt
120×sqrt-prod
70×distribute-lft-out
28×swap-sqr
22×associate-*r* associate-*l*
20×associate-/r* add-cbrt-cube add-exp-log
18×frac-sub
16×div-inv difference-of-squares
13×frac-times associate-*l/ associate-*r/
11×pow1 associate-/l/
9×unswap-sqr
7×associate-/l*
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×associate-/r/
2×clear-num frac-2neg flip3-- flip--
1×pow2 sub-neg flip3-+ pow-plus fma-neg diff-log div-sub prod-diff pow-prod-down frac-add pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 277
Calls
4 calls:
5.0ms
(/ 1.0 (sqrt x))
169.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
41.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
30.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series703.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(/ 1.0 (sqrt x))
507.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
50.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
87.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify3.0s

Counts
289 → 289
Iterations
IterNodes
done5000
24774
11356
0417

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
3.2b
(- (+ x 1.0) x)

rewrite279.0ms

Algorithm
rewrite-expression-head
Rules
319×*-un-lft-identity
296×times-frac
124×sqrt-prod
121×distribute-lft-out
116×add-sqr-sqrt
114×add-cube-cbrt
37×add-cbrt-cube add-exp-log
35×associate-/r/
34×div-inv
30×associate-*r/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
12×prod-diff
9×prod-exp cbrt-unprod add-log-exp
4×expm1-log1p-u pow1 fma-neg log1p-expm1-u
3×clear-num frac-2neg
2×sqrt-div diff-log distribute-lft-out--
1×sum-log sub-neg flip3-- frac-add associate--l+ flip-- difference-of-squares associate-/l/
Counts
4 → 272
Calls
4 calls:
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ 1.0 (sqrt x))
191.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
55.0ms
(- (+ x 1.0) x)

series772.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ 1.0 (sqrt (+ x 1.0)))
45.0ms
(/ 1.0 (sqrt x))
622.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
2.0ms
(- (+ x 1.0) x)

simplify1.8s

Counts
284 → 284
Iterations
IterNodes
done5000
11413
0496

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt (+ x 1.0)))
0.3b
(/ 1.0 (sqrt x))
0.5b
(/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0)))
4.2b
(/ (/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite200.0ms

Algorithm
rewrite-expression-head
Rules
298×*-un-lft-identity
297×times-frac
124×sqrt-prod
116×distribute-lft-out
106×add-sqr-sqrt add-cube-cbrt
58×add-cbrt-cube add-exp-log
37×associate-/r/
35×div-inv
32×associate-*r/
28×associate-/r*
21×cbrt-undiv div-exp
18×flip3-+ prod-exp cbrt-unprod flip-+
14×associate-/l*
4×expm1-log1p-u pow1 clear-num frac-2neg log1p-expm1-u add-log-exp
2×sqrt-div
1×frac-add associate-/l/
Counts
4 → 266
Calls
4 calls:
9.0ms
(/ 1.0 (sqrt (+ x 1.0)))
6.0ms
(/ 1.0 (sqrt x))
30.0ms
(/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0)))
139.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

series797.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ 1.0 (sqrt (+ x 1.0)))
47.0ms
(/ 1.0 (sqrt x))
59.0ms
(/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0)))
600.0ms
(/ (/ (* (* 1.0 1.0) 1.0) (* x (+ x 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))

simplify1.5s

Counts
278 → 278
Iterations
IterNodes
done5001
11328
0461

prune871.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes65.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done16
116
013

end0.0ms

sample1.6s

Algorithm
intervals
Results
560.0ms7925×body80nan
290.0ms1805×body640valid
209.0ms1171×body1280valid
204.0ms4036×body80valid
91.0ms665×body320valid
53.0ms323×body160valid