Details

Time bar (total: 14.5s)

sample46.0ms

Algorithm
intervals
Results
9.0ms66×body640valid
9.0ms282×body80nan
7.0ms42×body1280valid
4.0ms116×body80valid
2.0ms21×body320valid
1.0ms11×body160valid

simplify9.0ms

Counts
1 → 1
Iterations
IterNodes
done14
214
111
08

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.3b

localize12.0ms

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))
3.1b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite108.0ms

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-cbrt-cube add-exp-log distribute-lft-out
6×associate-/l* add-log-exp
5×pow1
4×sqrt-div div-inv
2×cbrt-undiv clear-num frac-2neg flip3-+ div-exp associate-/r/ flip-+
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log frac-sub flip--
Counts
4 → 133
Calls
4 calls:
8.0ms
(sqrt (+ x 1.0))
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ 1.0 (sqrt x))
77.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series381.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(sqrt (+ x 1.0))
87.0ms
(/ 1.0 (sqrt (+ x 1.0)))
49.0ms
(/ 1.0 (sqrt x))
194.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify1.2s

Counts
145 → 145
Iterations
IterNodes
done5001
21655
1462
0216

prune690.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(* (sqrt (+ x 1.0)) (sqrt x))
3.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite163.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×sqrt-prod
20×*-un-lft-identity
18×add-cbrt-cube add-exp-log
9×pow1 add-cube-cbrt
7×associate-*l*
6×sqrt-div associate-*r* add-log-exp
5×prod-exp cbrt-unprod
4×cbrt-undiv div-exp associate-*l/ 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/ associate-/r/ flip-- associate-/l/
1×rem-sqrt-square clear-num associate-/r* sub-neg frac-2neg times-frac sqrt-unprod diff-log *-commutative div-inv associate-/l*
Counts
4 → 93
Calls
4 calls:
11.0ms
(sqrt (+ x 1.0))
66.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
27.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
53.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series532.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(sqrt (+ x 1.0))
336.0ms
(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt (+ x 1.0)) (sqrt x)))
61.0ms
(* (sqrt (+ x 1.0)) (sqrt x))
85.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify1.4s

Counts
105 → 105
Iterations
IterNodes
done5000
23032
1531
0192

prune525.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite272.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
43×distribute-lft-out
39×sqrt-prod
31×times-frac
29×add-sqr-sqrt add-cbrt-cube add-exp-log
21×add-cube-cbrt
9×cbrt-undiv div-exp
8×pow1 prod-exp cbrt-unprod
7×associate-/r* associate-*l* distribute-lft-out--
6×associate-*r* associate-/l* add-log-exp
5×flip3-+ flip-+
4×sqrt-div associate-*l/ associate-/r/ unswap-sqr
3×pow-prod-down associate-/l/
2×clear-num frac-2neg sqrt-pow1 pow1/2 div-inv
1×+-commutative associate-+r- sum-log sqrt-unprod div-sub associate-*r/ *-commutative
Counts
4 → 133
Calls
4 calls:
49.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
124.0ms
(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
52.0ms
(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
41.0ms
(* (sqrt (+ x 1.0)) (sqrt x))

series1.0s

Counts
4 → 12
Calls
4 calls:
93.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
191.0ms
(/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
640.0ms
(/ (* 1.0 (/ (+ 1.0 (- x x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt (+ x 1.0)) (sqrt x)))
81.0ms
(* (sqrt (+ x 1.0)) (sqrt x))

simplify2.4s

Counts
145 → 145
Iterations
IterNodes
done5002
24982
1760
0269

prune697.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
0.3b
(cbrt (sqrt (+ 1.0 x)))
0.3b
(cbrt (sqrt (+ x 1.0)))
0.3b
(cbrt (sqrt (+ x 1.0)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
69×cbrt-prod
44×add-sqr-sqrt
42×*-un-lft-identity
40×sqrt-prod
22×add-cube-cbrt
18×cbrt-div sqrt-div
14×swap-sqr
11×pow1
10×associate-*r* associate-*l*
9×flip3-+ pow1/3 flip-+ distribute-lft-out unswap-sqr
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp
2×pow-prod-down associate-*l/ associate-*r/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 120
Calls
4 calls:
35.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
6.0ms
(cbrt (sqrt (+ 1.0 x)))
8.0ms
(cbrt (sqrt (+ x 1.0)))
8.0ms
(cbrt (sqrt (+ x 1.0)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(* (cbrt (sqrt (+ x 1.0))) (cbrt (sqrt (+ x 1.0))))
120.0ms
(cbrt (sqrt (+ 1.0 x)))
98.0ms
(cbrt (sqrt (+ x 1.0)))
107.0ms
(cbrt (sqrt (+ x 1.0)))

simplify1.2s

Counts
132 → 132
Iterations
IterNodes
done5000
21736
1429
0205

prune816.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done17
117
012

end0.0ms

sample2.3s

Algorithm
intervals
Results
490.0ms659×body320valid
448.0ms1837×body640valid
376.0ms8079×body80nan
365.0ms1103×body1280valid
270.0ms4114×body80valid
25.0ms287×body160valid