Details

Time bar (total: 16.2s)

sample84.0ms

Algorithm
intervals
Results
38.0ms72×body1280valid
17.0ms54×body640valid
6.0ms19×body2560valid
5.0ms26×body320valid
3.0ms73×body80valid
1.0ms12×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.6b

localize11.0ms

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))

rewrite14.0ms

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:
6.0ms
(+ x (sqrt (fma x x 1.0)))
5.0ms
(log (+ x (sqrt (fma x x 1.0))))
1.0ms
(sqrt (fma x x 1.0))

series490.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(+ x (sqrt (fma x x 1.0)))
295.0ms
(log (+ x (sqrt (fma x x 1.0))))
72.0ms
(sqrt (fma x x 1.0))

simplify1.2s

Counts
58 → 58
Iterations
IterNodes
done5001
21087
1289
0126

prune348.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
21×pow1
7×add-cbrt-cube add-exp-log
6×pow-plus pow-prod-up
4×add-sqr-sqrt
3×*-un-lft-identity associate-*r* pow-prod-down prod-exp add-cube-cbrt cbrt-unprod
2×pow2 expm1-log1p-u pow-sqr log1p-expm1-u add-log-exp
1×associate-*l* pow3 *-commutative fma-udef unswap-sqr
Counts
2 → 40
Calls
2 calls:
1.0ms
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
29.0ms
(* (* x x) x)

series214.0ms

Counts
2 → 6
Calls
2 calls:
145.0ms
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
69.0ms
(* (* x x) x)

simplify1.1s

Counts
46 → 46
Iterations
IterNodes
done5000
2791
1139
060

prune265.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
26×*-un-lft-identity
24×pow1
22×add-cube-cbrt
21×prod-diff
19×add-exp-log
18×add-cbrt-cube
12×times-frac
6×pow-plus prod-exp pow-prod-up cbrt-unprod add-log-exp
5×log-prod
4×expm1-log1p-u log1p-expm1-u div-inv
3×cbrt-undiv fma-neg div-exp associate-*r* pow-prod-down associate-/l*
2×pow2 log-div flip3-- pow-sqr flip-- distribute-lft-out-- difference-of-squares
1×clear-num associate-/r* sub-neg frac-2neg diff-log rem-log-exp associate-*l* pow3 associate--l+ log-pow *-commutative fma-udef unswap-sqr
Counts
4 → 114
Calls
4 calls:
31.0ms
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x)))
25.0ms
(* (* x x) x)
16.0ms
(/ 0.125 (* (* x x) x))
17.0ms
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x))))

series426.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x)))
50.0ms
(* (* x x) x)
68.0ms
(/ 0.125 (* (* x x) x))
253.0ms
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x))))

simplify2.5s

Counts
126 → 126
Iterations
IterNodes
done5000
23401
1529
0213

prune532.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

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)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.7b
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite853.0ms

Algorithm
rewrite-expression-head
Rules
358×add-sqr-sqrt
284×times-frac
270×*-un-lft-identity
241×prod-diff
208×add-cube-cbrt
93×associate--l+
68×unpow-prod-down
60×difference-of-squares
32×distribute-lft-out--
28×div-inv
24×sqr-pow
19×add-exp-log
15×add-cbrt-cube
9×log-prod add-log-exp
8×associate-/r* frac-sub
6×fma-neg div-exp associate-/l*
5×pow1 log-div
4×expm1-log1p-u cbrt-undiv flip3-- log1p-expm1-u flip--
3×diff-log prod-exp cbrt-unprod
2×clear-num sub-neg frac-2neg
1×associate--l- pow-to-exp rem-log-exp pow-exp log-pow
Counts
4 → 371
Calls
4 calls:
9.0ms
(/ 0.0625 (pow x 5))
24.0ms
(/ 0.125 (* (* x x) x))
277.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
503.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ 0.0625 (pow x 5))
52.0ms
(/ 0.125 (* (* x x) x))
274.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
69.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

simplify1.2s

Counts
383 → 383
Iterations
IterNodes
done5001
11483
0584

prune2.4s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes77.0ms

Accuracy

99.5% (0.2b remaining)

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

bsearch157.0ms

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

simplify11.0ms

Iterations
IterNodes
done35
135
033

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.7s2395×body1280valid
597.0ms1540×body640valid
528.0ms2087×body80valid
333.0ms772×body2560valid
211.0ms796×body320valid
58.0ms410×body160valid