Details

Time bar (total: 18.6s)

sample71.0ms

Algorithm
intervals
Results
13.0ms55×body640valid
12.0ms253×body80nan
10.0ms34×body1280valid
9.0ms142×body80valid
2.0ms13×body320valid
1.0ms12×body160valid

simplify10.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.6b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite177.0ms

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))
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
5.0ms
(/ 1.0 (sqrt x))
96.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(sqrt (+ x 1.0))
110.0ms
(/ 1.0 (sqrt (+ x 1.0)))
75.0ms
(/ 1.0 (sqrt x))
183.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify2.7s

Counts
770 → 770
Iterations
IterNodes
done5000
24935
11587
0702

prune3.3s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 16.6b

localize20.0ms

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))))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
2.5b
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

rewrite103.0ms

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:
9.0ms
(sqrt (+ x 1.0))
54.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
18.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

series612.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(sqrt (+ x 1.0))
377.0ms
(/ (- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)) (* (sqrt x) (sqrt (+ x 1.0))))
64.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
137.0ms
(- (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))

simplify2.3s

Counts
110 → 110
Iterations
IterNodes
done5001
22858
1592
0206

prune807.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 16.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (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)))

rewrite209.0ms

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:
28.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
63.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
29.0ms
(* (* (sqrt x) 1.0) (* (sqrt x) 1.0))
84.0ms
(- (* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0)))) (* (* (sqrt x) 1.0) (* (sqrt x) 1.0)))

series212.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
60.0ms
(* (* 1.0 (sqrt (+ x 1.0))) (* 1.0 (sqrt (+ x 1.0))))
40.0ms
(* (* (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)))

simplify2.1s

Counts
144 → 144
Iterations
IterNodes
done5000
22222
1498
0183

prune722.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
0.1b
(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
0.2b
(* (sqrt x) (sqrt (+ x 1.0)))
0.6b
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube add-exp-log
19×add-sqr-sqrt
18×associate-*r/
14×flip3-+ sqrt-div flip-+
13×pow1 *-un-lft-identity
11×add-cube-cbrt sqrt-prod
10×associate-*r*
8×frac-times associate-/r/
7×associate-*l* prod-exp cbrt-unprod
6×pow-prod-down add-log-exp
4×expm1-log1p-u associate-*l/ log1p-expm1-u unswap-sqr
3×cbrt-undiv times-frac div-exp associate-/l*
2×sqrt-pow1 pow1/2 *-commutative
1×distribute-rgt-in +-commutative clear-num associate-/r* sum-log fma-def frac-2neg distribute-lft-in sqrt-unprod div-inv distribute-lft-out
Counts
4 → 112
Calls
4 calls:
11.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
64.0ms
(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
20.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
53.0ms
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
105.0ms
(+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))
296.0ms
(* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0)))
61.0ms
(* (sqrt x) (sqrt (+ x 1.0)))
585.0ms
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))

simplify1.2s

Counts
124 → 124
Iterations
IterNodes
done5000
1853
0272

prune492.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes85.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done19
119
012

end0.0ms

sample1.8s

Algorithm
intervals
Results
333.0ms7946×body80nan
328.0ms1154×body1280valid
302.0ms313×body160valid
287.0ms1914×body640valid
175.0ms4059×body80valid
54.0ms560×body320valid