Details

Time bar (total: 14.2s)

sample93.0ms

Algorithm
intervals
Results
39.0ms72×body1280valid
28.0ms54×body640valid
7.0ms19×body2560valid
5.0ms26×body320valid
3.0ms73×body80valid
1.0ms12×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
07232
110207
done10207

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (fma x x 1.0)))
2.7b
(log (+ x (sqrt (fma x x 1.0))))
13.8b
(sqrt (fma x x 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube sqrt-prod log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 49
Calls
3 calls:
11.0ms
(+ x (sqrt (fma x x 1.0)))
10.0ms
(log (+ x (sqrt (fma x x 1.0))))
2.0ms
(sqrt (fma x x 1.0))

series476.0ms

Counts
3 → 9
Calls
3 calls:
124.0ms
(+ x (sqrt (fma x x 1.0)))
275.0ms
(log (+ x (sqrt (fma x x 1.0))))
77.0ms
(sqrt (fma x x 1.0))

simplify1.1s

Counts
58 → 58
Iterations

Useful iterations: done (1.1s)

IterNodesCost
012618143
128914293
2108713617
done500113377

prune361.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
7×add-cbrt-cube add-exp-log
5×pow-prod-up
4×add-sqr-sqrt
3×*-un-lft-identity associate-*l* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×expm1-log1p-u log1p-expm1-u add-log-exp
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative fma-udef unswap-sqr
Counts
2 → 36
Calls
2 calls:
0.0ms
(fma (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) -1/6 (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
13.0ms
(* x (* x x))

series218.0ms

Counts
2 → 6
Calls
2 calls:
174.0ms
(fma (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) -1/6 (+ (/ x (sqrt 1.0)) (log (sqrt 1.0))))
44.0ms
(* x (* x x))

simplify1.1s

Counts
42 → 42
Iterations

Useful iterations: 2 (154.0ms)

IterNodesCost
0609920
11328742
26508305
done50018305

prune199.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 2 x (- (/ 0.5 x) (/ 0.125 (* x (* x x)))))
0.1b
(* x (* x x))
0.3b
(/ 0.125 (* x (* x x)))
9.0b
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (* x (* x x))))))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log
18×add-cbrt-cube
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×prod-exp cbrt-unprod
5×pow-prod-up
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv log-prod times-frac div-exp associate-*l* pow-prod-down associate-/l*
1×pow2 clear-num associate-/r* frac-2neg pow-plus cube-unmult rem-log-exp associate-*r* pow-sqr log-pow *-commutative fma-udef div-inv unswap-sqr
Counts
4 → 75
Calls
4 calls:
1.0ms
(fma 2 x (- (/ 0.5 x) (/ 0.125 (* x (* x x)))))
25.0ms
(* x (* x x))
26.0ms
(/ 0.125 (* x (* x x)))
2.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (* x (* x x))))))

series421.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma 2 x (- (/ 0.5 x) (/ 0.125 (* x (* x x)))))
40.0ms
(* x (* x x))
64.0ms
(/ 0.125 (* x (* x x)))
252.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (* x (* x x))))))

simplify1.7s

Counts
87 → 87
Iterations

Useful iterations: 2 (685.0ms)

IterNodesCost
014223037
134419591
2233518469
done500018469

prune422.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (* x (* x x)))
11.2b
(log (- (- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
19.7b
(- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5)))

rewrite501.0ms

Algorithm
rewrite-expression-head
Rules
253×times-frac
188×add-sqr-sqrt
180×*-un-lft-identity
175×prod-diff
173×add-cube-cbrt
76×unpow-prod-down
35×div-inv
26×sqr-pow
19×add-exp-log
15×add-cbrt-cube
8×associate-/r*
7×log-prod fma-neg
6×div-exp associate-/l* add-log-exp difference-of-squares
5×pow1 log-div frac-sub
4×expm1-log1p-u cbrt-undiv log1p-expm1-u distribute-lft-out--
3×flip3-- prod-exp cbrt-unprod flip--
2×clear-num frac-2neg
1×pow-to-exp sub-neg diff-log rem-log-exp pow-exp log-pow
Counts
4 → 297
Calls
4 calls:
6.0ms
(/ 0.0625 (pow x 5))
25.0ms
(/ 0.125 (* x (* x x)))
346.0ms
(log (- (- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
107.0ms
(- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5)))

series557.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ 0.0625 (pow x 5))
83.0ms
(/ 0.125 (* x (* x x)))
224.0ms
(log (- (- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5))) (/ 0.5 x)))
174.0ms
(- (/ 0.125 (* x (* x x))) (/ 0.0625 (pow x 5)))

simplify1.7s

Counts
309 → 309
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0556295712
11374269693
done5001253246

prune1.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.1b

bsearch108.0ms

Steps
ItersRangePoint
9
5.1798647897020696e-05
160.65039477392645
0.8907247814494134
10
-83422883652835.42
-0.9341403346610884
-1.02659151339998

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0331320
1361320
done361320

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.5s2395×body1280valid
958.0ms1540×body640valid
363.0ms772×body2560valid
158.0ms796×body320valid
143.0ms2087×body80valid
49.0ms410×body160valid