Details

Time bar (total: 22.7s)

sample75.0ms

Algorithm
intervals
Results
15.0ms59×body640valid
13.0ms248×body80nan
13.0ms39×body1280valid
8.0ms124×body80valid
4.0ms22×body320valid
2.0ms12×body160valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
08242
111242
214242
done14242

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.9b

localize32.0ms

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))
2.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite299.0ms

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:
11.0ms
(sqrt (+ x 1.0))
19.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (sqrt x))
139.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series410.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sqrt (+ x 1.0))
128.0ms
(/ 1.0 (sqrt (+ x 1.0)))
53.0ms
(/ 1.0 (sqrt x))
175.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify3.8s

Counts
770 → 770
Iterations

Useful iterations: done (3.6s)

IterNodesCost
0702663291
11587578037
23579523469
done5000522489

prune3.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 19.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
2.6b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
15×*-un-lft-identity sqrt-prod
11×add-cbrt-cube add-exp-log add-cube-cbrt
9×pow1
7×associate-*r*
6×sqrt-div associate-*l* add-log-exp
4×expm1-log1p-u associate-*r/ log1p-expm1-u unswap-sqr
3×sqrt-pow1 flip3-+ times-frac pow1/2 pow-prod-down flip-+ associate-/l*
2×cbrt-undiv flip3-- div-exp prod-exp associate-/r/ cbrt-unprod flip-- distribute-lft-out associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg fma-neg sqrt-unprod diff-log div-sub prod-diff *-commutative hypot-def div-inv
Counts
4 → 98
Calls
4 calls:
11.0ms
(sqrt (+ x 1.0))
69.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
14.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series629.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(sqrt (+ x 1.0))
407.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
68.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
123.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify2.6s

Counts
110 → 110
Iterations

Useful iterations: done (2.6s)

IterNodesCost
020638473
159132338
2218129517
done500529309

prune756.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 19.1b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt x) (sqrt (+ x 1.0)))
0.3b
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
0.5b
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
1.7b
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

rewrite299.0ms

Algorithm
rewrite-expression-head
Rules
86×pow1
37×pow-prod-down
30×add-cbrt-cube add-exp-log
17×prod-exp cbrt-unprod
16×add-sqr-sqrt associate-*r/
14×sqrt-div
11×sqrt-prod
10×*-un-lft-identity
9×associate-*r*
8×associate-*l* pow-sqr pow-prod-up add-cube-cbrt
7×flip3-+ flip-+
6×add-log-exp
4×expm1-log1p-u frac-times pow-plus log1p-expm1-u unswap-sqr
3×*-commutative
2×pow2 sqrt-pow1 pow1/2 swap-sqr associate-*l/
1×sub-neg flip3-- fma-neg sqrt-unprod diff-log prod-diff flip-- distribute-lft-out difference-of-squares
Counts
4 → 132
Calls
4 calls:
26.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
99.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
58.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
111.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series204.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
48.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
36.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
21.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

simplify2.3s

Counts
144 → 144
Iterations

Useful iterations: done (2.3s)

IterNodesCost
018336176
149128744
2152424845
done500324642

prune708.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
38×add-sqr-sqrt
32×*-un-lft-identity
30×add-cube-cbrt
20×add-cbrt-cube add-exp-log
18×associate-/l*
11×sqrt-prod
8×pow1 associate-/r/
7×cbrt-undiv div-exp associate-*r*
6×flip3-+ associate-*l* flip-+ add-log-exp
4×expm1-log1p-u associate-/r* sqrt-div associate-*r/ log1p-expm1-u div-inv unswap-sqr
3×pow-prod-down prod-exp cbrt-unprod
2×clear-num frac-2neg sqrt-pow1 pow1/2
1×+-commutative sum-log fma-def sqrt-unprod *-commutative distribute-lft-out associate-/l/
Counts
4 → 134
Calls
4 calls:
18.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
18.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
60.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
34.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

series1.3s

Counts
4 → 12
Calls
4 calls:
156.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
275.0ms
(/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
791.0ms
(/ (/ 1.0 (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))) (* (sqrt x) (sqrt (+ x 1.0))))
101.0ms
(* (sqrt x) (sqrt (+ x 1.0)))

simplify3.1s

Counts
146 → 146
Iterations

Useful iterations: done (3.0s)

IterNodesCost
028867312
180857012
2283854964
done500354801

prune671.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes136.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
010337
113337
done13337

end0.0ms

sample2.0s

Algorithm
intervals
Results
569.0ms1105×body1280valid
418.0ms1837×body640valid
408.0ms7971×body80nan
250.0ms4088×body80valid
79.0ms664×body320valid
25.0ms306×body160valid