Details

Time bar (total: 17.9s)

sample114.0ms

Algorithm
intervals
Results
49.0ms72×body1280valid
25.0ms57×body640valid
15.0ms28×body2560valid
6.0ms25×body320valid
4.0ms64×body80valid
1.0ms10×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1108
done108

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.7b
(+ x (sqrt (+ (* x x) 1.0)))
2.7b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.5b
(sqrt (+ (* x x) 1.0))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
9×add-sqr-sqrt
8×add-log-exp
7×add-cube-cbrt
6×pow1
5×add-exp-log
4×expm1-log1p-u log-prod fma-def flip3-+ add-cbrt-cube flip-+ log1p-expm1-u
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow hypot-def
Counts
4 → 66
Calls
4 calls:
22.0ms
(+ (* x x) 1.0)
35.0ms
(+ x (sqrt (+ (* x x) 1.0)))
34.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
20.0ms
(sqrt (+ (* x x) 1.0))

series497.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (* x x) 1.0)
88.0ms
(+ x (sqrt (+ (* x x) 1.0)))
294.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
52.0ms
(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts
78 → 78
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0149949
1372787
21657707
done5001695

prune345.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 1 expressions with local error:

0.3b
(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series214.0ms

Counts
1 → 3
Calls
1 calls:
214.0ms
(fma -1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify1.0s

Counts
13 → 13
Iterations

Useful iterations: done (1.0s)

IterNodesCost
025295
151295
2176256
31248256
done5000255

prune75.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (pow x 3))
13.6b
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.7b
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
1674×add-sqr-sqrt
1602×times-frac
1026×*-un-lft-identity
895×prod-diff
848×add-cube-cbrt
522×associate--l+
330×unpow-prod-down
268×difference-of-squares
181×cube-prod
146×sqr-pow
70×div-inv
62×distribute-lft-out--
43×cube-mult unpow3
19×associate-/r*
15×add-exp-log fma-neg
10×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp associate-/l*
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv pow-to-exp sub-neg frac-2neg pow-exp clear-num
1×associate--l- rem-log-exp log-pow
Counts
4 → 1078
Calls
4 calls:
15.0ms
(/ 0.0625 (pow x 5))
17.0ms
(/ 0.125 (pow x 3))
472.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
957.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(/ 0.0625 (pow x 5))
66.0ms
(/ 0.125 (pow x 3))
284.0ms
(log (- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
91.0ms
(- (- (/ 0.125 (pow x 3)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.1s

Counts
1090 → 1090
Iterations

Useful iterations: done (1.0s)

IterNodesCost
081244329
1192440129
done500132329

prune4.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.4b
(/ 0.125 (pow x 3))
10.2b
(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
888×times-frac
633×add-sqr-sqrt
608×*-un-lft-identity
602×add-cube-cbrt
520×prod-diff
131×unpow-prod-down cube-prod
55×div-inv
45×sqr-pow
43×cube-mult unpow3
13×fma-neg
12×associate-/r*
10×difference-of-squares
9×add-exp-log
5×add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u log-prod div-exp log1p-expm1-u associate-/l*
2×distribute-lft-out--
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip--
Counts
3 → 641
Calls
3 calls:
66.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
12.0ms
(/ 0.125 (pow x 3))
3.0ms
(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series416.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
56.0ms
(/ 0.125 (pow x 3))
241.0ms
(log (fma x 2 (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify677.0ms

Counts
650 → 650
Iterations

Useful iterations: done (635.0ms)

IterNodesCost
074231264
1172525528
done500020811

prune1.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes31.0ms

Accuracy

100% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 32.2b

bsearch114.0ms

Steps
ItersRangePoint
9
0.00015484893005477947
28918.939680702064
0.9042263775546854
10
-2676750800.736259
-2.9526231381329305e-09
-0.994187787075435

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13455
done3455

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.4s2245×body1280valid
989.0ms1646×body640valid
338.0ms799×body2560valid
191.0ms762×body320valid
106.0ms2166×body80valid
86.0ms382×body160valid