Details

Time bar (total: 15.6s)

sample104.0ms

Algorithm
intervals
Results
48.0ms74×body1280valid
21.0ms54×body640valid
11.0ms28×body2560valid
5.0ms23×body320valid
4.0ms62×body80valid
2.0ms15×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
079
1108
done108

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize38.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ (sqrt (fma x x 1.0)) x)
4.8b
(log (+ (sqrt (fma x x 1.0)) x))
15.8b
(sqrt (fma x x 1.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
6×fma-def sqrt-prod
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 52
Calls
3 calls:
9.0ms
(+ (sqrt (fma x x 1.0)) x)
15.0ms
(log (+ (sqrt (fma x x 1.0)) x))
3.0ms
(sqrt (fma x x 1.0))

series505.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(+ (sqrt (fma x x 1.0)) x)
314.0ms
(log (+ (sqrt (fma x x 1.0)) x))
74.0ms
(sqrt (fma x x 1.0))

simplify2.1s

Counts
61 → 61
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0125701
1283639
2768573
32364571
done5000556

prune231.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (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 (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series178.0ms

Counts
1 → 3
Calls
1 calls:
178.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify932.0ms

Counts
13 → 13
Iterations

Useful iterations: done (931.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune84.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
13.4b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
18.7b
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
480×*-un-lft-identity
367×times-frac
244×add-sqr-sqrt
218×add-cube-cbrt
200×prod-diff
84×distribute-lft-out
80×unpow-prod-down
68×cube-prod
40×fma-neg
28×sqr-pow
22×cube-mult unpow3
19×associate-/r*
15×add-exp-log
11×log-prod
10×difference-of-squares
9×add-log-exp
8×add-cbrt-cube div-inv
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 408
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
9.0ms
(/ 0.125 (pow x 3))
185.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
237.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series431.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(/ 0.0625 (pow x 5))
57.0ms
(/ 0.125 (pow x 3))
247.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
66.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.8s

Counts
420 → 420
Iterations

Useful iterations: done (1.8s)

IterNodesCost
046617338
1101711893
228049355
done50008895

prune848.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log 2) (/ 0.25 (* x x)))
0.1b
(/ 0.09375 (pow x 4))
0.2b
(/ 0.25 (* x x))
6.8b
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

rewrite377.0ms

Algorithm
rewrite-expression-head
Rules
192×*-un-lft-identity
172×add-sqr-sqrt
145×prod-diff
123×times-frac
120×add-cube-cbrt
102×associate--r+
53×unpow-prod-down
52×pow1
48×log-pow
28×distribute-lft-out
25×distribute-lft-out--
21×difference-of-squares sqr-pow
14×add-exp-log
13×add-log-exp
11×add-cbrt-cube
8×associate-/r*
6×diff-log div-inv associate-/l*
5×fma-neg div-exp
4×expm1-log1p-u fma-def frac-sub log1p-expm1-u
3×cbrt-undiv associate-+l+ log-prod flip3-- flip3-+ sum-log flip-- flip-+
2×sub-neg frac-2neg clear-num
1×+-commutative pow-to-exp pow-exp prod-exp associate--l+ cbrt-unprod associate--r-
Counts
4 → 277
Calls
4 calls:
23.0ms
(+ (log 2) (/ 0.25 (* x x)))
12.0ms
(/ 0.09375 (pow x 4))
13.0ms
(/ 0.25 (* x x))
298.0ms
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

series569.0ms

Counts
4 → 12
Calls
4 calls:
363.0ms
(+ (log 2) (/ 0.25 (* x x)))
55.0ms
(/ 0.09375 (pow x 4))
29.0ms
(/ 0.25 (* x x))
121.0ms
(- (+ (log 2) (/ 0.25 (* x x))) (- (/ 0.09375 (pow x 4)) (log x)))

simplify1.9s

Counts
289 → 289
Iterations

Useful iterations: 2 (922.0ms)

IterNodesCost
04468680
111567462
233326571
done50006571

prune1.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

regimes45.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.7b

bsearch134.0ms

Steps
ItersRangePoint
9
3.244205803610274e-06
1902.9075791774285
0.9479026978334683
8
-45.38980787391071
-0.005411406272604966
-0.998226736869587

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04259
14559
done4559

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.5s2333×body1280valid
1.2s1587×body640valid
337.0ms777×body2560valid
202.0ms755×body320valid
110.0ms2109×body80valid
56.0ms439×body160valid