Details

Time bar (total: 11.3s)

sample36.0ms

Algorithm
intervals
Results
7.0ms262×body80nan
5.0ms44×body1280valid
4.0ms46×body640valid
4.0ms140×body80valid
1.0ms20×body320valid
0.0ms6×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
8.0ms
(sqrt (+ x 1.0))
85.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series116.0ms

Counts
2 → 6
Calls
2 calls:
34.0ms
(sqrt (+ x 1.0))
82.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify734.0ms

Counts
95 → 95
Iterations

Useful iterations: done (730.0ms)

IterNodesCost
01371993
13161446
210401125
done5000951

prune160.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt x) (sqrt (+ x 1.0)))
0.2b
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
32×distribute-lft-out
31×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
6×fma-def associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 93
Calls
3 calls:
8.0ms
(sqrt (+ x 1.0))
27.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
65.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

series281.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(sqrt (+ x 1.0))
74.0ms
(+ (sqrt x) (sqrt (+ x 1.0)))
153.0ms
(/ (+ 1.0 0) (+ (sqrt x) (sqrt (+ x 1.0))))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01691453
14281178
219951093
done50011085

prune428.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.2b
(/ (+ 1.0 0) (+ (sqrt x) (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
0.3b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
63×add-sqr-sqrt
55×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
29×add-cube-cbrt
20×pow1/2
18×swap-sqr
12×times-frac distribute-lft-out
10×flip3-+ associate-*r* associate-*l* flip-+
9×pow-prod-up unswap-sqr
8×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times rem-sqrt-square log1p-expm1-u associate-/l* add-log-exp
3×associate-/r*
2×associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 175
Calls
4 calls:
18.0ms
(sqrt (sqrt (+ x 1.0)))
17.0ms
(sqrt (sqrt (+ x 1.0)))
33.0ms
(/ (+ 1.0 0) (+ (sqrt x) (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
77.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series718.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(sqrt (sqrt (+ x 1.0)))
90.0ms
(sqrt (sqrt (+ x 1.0)))
495.0ms
(/ (+ 1.0 0) (+ (sqrt x) (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))))
44.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify2.1s

Counts
187 → 187
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02663296
16471967
229301850
done50021834

prune484.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
22.0ms
(* (cbrt x) (cbrt x))
1.0ms
(cbrt x)
2.0ms
(cbrt x)
2.0ms
(cbrt x)

series1.2s

Counts
4 → 12
Calls
4 calls:
339.0ms
(* (cbrt x) (cbrt x))
287.0ms
(cbrt x)
259.0ms
(cbrt x)
296.0ms
(cbrt x)

simplify1.1s

Counts
93 → 93
Iterations

Useful iterations: done (1.1s)

IterNodesCost
065554
1143443
2719423
done5000409

prune374.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.0b

regimes93.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
0911
1129
2139
done139

end0.0ms

sample1.8s

Algorithm
intervals
Results
437.0ms8084×body80nan
389.0ms1742×body1280valid
260.0ms1252×body640valid
158.0ms4103×body80valid
97.0ms599×body320valid
22.0ms304×body160valid