Details

Time bar (total: 18.4s)

sample42.0ms

Algorithm
intervals
Results
10.0ms60×body1280valid
9.0ms267×body80nan
5.0ms40×body640valid
4.0ms116×body80valid
3.0ms28×body320valid
1.0ms12×body160valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
312
212
111
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1))
3.4b
(- (sqrt (+ x 1)) (sqrt x))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
55×*-un-lft-identity
43×add-sqr-sqrt
42×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×expm1-log1p-u add-cbrt-cube sqrt-div add-exp-log hypot-def insert-posit16 log1p-expm1-u
1×rem-sqrt-square sub-neg sqrt-pow1 flip3-+ flip3-- pow1/2 diff-log flip-+ flip--
Counts
2 → 92
Calls
2 calls:
8.0ms
(sqrt (+ x 1))
56.0ms
(- (sqrt (+ x 1)) (sqrt x))

series128.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(sqrt (+ x 1))
103.0ms
(- (sqrt (+ x 1)) (sqrt x))

simplify2.9s

Counts
98 → 98
Iterations
IterNodes
44001
31450
2620
1285
0134

prune827.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1))
0.0b
(+ (sqrt (+ x 1)) (sqrt x))
0.2b
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
28×sqrt-prod
22×distribute-lft-out
21×add-sqr-sqrt
18×times-frac
17×add-cube-cbrt
7×fma-def add-exp-log
6×associate-/r*
5×pow1 add-cbrt-cube add-log-exp
3×expm1-log1p-u flip3-+ flip-+ insert-posit16 log1p-expm1-u associate-/l*
2×sqrt-div div-exp associate-/r/ hypot-def
1×cbrt-undiv +-commutative rem-sqrt-square rec-exp clear-num sum-log frac-2neg sqrt-pow1 pow1/2 1-exp div-inv pow-flip inv-pow
Counts
3 → 93
Calls
3 calls:
6.0ms
(sqrt (+ x 1))
24.0ms
(+ (sqrt (+ x 1)) (sqrt x))
34.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

series229.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1))
70.0ms
(+ (sqrt (+ x 1)) (sqrt x))
123.0ms
(/ 1 (+ (sqrt (+ x 1)) (sqrt x)))

simplify1.5s

Counts
102 → 102
Iterations
IterNodes
42651
31150
2574
1257
0126

prune867.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1)))
0.1b
(sqrt (sqrt (+ x 1)))
0.2b
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
0.3b
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×pow1 sqrt-div
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l* add-exp-log
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×expm1-log1p-u frac-times rem-sqrt-square insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×div-exp associate-*l/ associate-*r/ associate-/r/
1×pow2 cbrt-undiv rec-exp clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod 1-exp prod-exp *-commutative cbrt-unprod div-inv pow-flip inv-pow
Counts
4 → 177
Calls
4 calls:
11.0ms
(sqrt (sqrt (+ x 1)))
12.0ms
(sqrt (sqrt (+ x 1)))
69.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
46.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series256.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(sqrt (sqrt (+ x 1)))
62.0ms
(sqrt (sqrt (+ x 1)))
86.0ms
(/ 1 (+ (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt x)))
43.0ms
(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify1.1s

Counts
189 → 189
Iterations
IterNodes
32454
21046
1449
0217

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (sqrt (+ x 1))))
0.2b
(/ 1 (+ (* (sqrt (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))) (sqrt x)))
0.2b
(* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))
0.2b
(* (sqrt (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1)))))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
180×sqrt-div
143×sqrt-pow1
113×sqrt-prod
76×pow1
59×add-sqr-sqrt
57×pow-prod-up
55×pow1/2
35×flip3-+ flip-+
34×*-un-lft-identity
32×frac-times
26×associate-*l* add-cube-cbrt
16×pow-prod-down associate-*r/
15×add-exp-log
13×add-cbrt-cube
12×unswap-sqr
11×associate-*r*
10×associate-*l/
9×times-frac
6×pow-plus cube-unmult
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
3×rem-sqrt-square associate-/r* sqrt-unprod associate-/l*
2×div-exp associate-/r/ *-commutative
1×cbrt-undiv rec-exp clear-num frac-2neg 1-exp div-inv pow-flip inv-pow
Counts
4 → 233
Calls
4 calls:
13.0ms
(sqrt (sqrt (sqrt (+ x 1))))
145.0ms
(/ 1 (+ (* (sqrt (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))) (sqrt x)))
37.0ms
(* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))
108.0ms
(* (sqrt (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1)))))

series251.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(sqrt (sqrt (sqrt (+ x 1))))
113.0ms
(/ 1 (+ (* (sqrt (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))) (sqrt x)))
55.0ms
(* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1))))
34.0ms
(* (sqrt (sqrt (sqrt (+ x 1)))) (* (sqrt (sqrt (sqrt (+ x 1)))) (sqrt (sqrt (+ x 1)))))

simplify2.4s

Counts
245 → 245
Iterations
IterNodes
33884
21955
1820
0338

prune3.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes80.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
211
111
07

end0.0ms

sample1.9s

Algorithm
intervals
Results
577.0ms1788×body1280valid
452.0ms8102×body80nan
316.0ms4068×body80valid
259.0ms1234×body640valid
87.0ms607×body320valid
34.0ms303×body160valid