Details

Time bar (total: 15.6s)

sample116.0ms

Algorithm
intervals
Results
61.0ms83×body1280valid
19.0ms46×body640valid
13.0ms26×body2560valid
6.0ms26×body320valid
3.0ms61×body80valid
2.0ms14×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.6b
(+ x (sqrt (fma x x 1.0)))
3.1b
(log (+ x (sqrt (fma x x 1.0))))
14.0b
(sqrt (fma x x 1.0))

rewrite20.0ms

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:
9.0ms
(+ x (sqrt (fma x x 1.0)))
8.0ms
(log (+ x (sqrt (fma x x 1.0))))
2.0ms
(sqrt (fma x x 1.0))

series431.0ms

Counts
3 → 9
Calls
3 calls:
94.0ms
(+ x (sqrt (fma x x 1.0)))
250.0ms
(log (+ x (sqrt (fma x x 1.0))))
87.0ms
(sqrt (fma x x 1.0))

simplify1.2s

Counts
58 → 58
Iterations
IterNodes
done5001
21087
1289
0126

prune453.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 2 expressions with local error:

0.1b
(* (* x x) x)
0.3b
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite30.0ms

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:
27.0ms
(* (* x x) x)
1.0ms
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series234.0ms

Counts
2 → 6
Calls
2 calls:
58.0ms
(* (* x x) x)
177.0ms
(fma (/ (/ (* (* x x) x) 1.0) (sqrt 1.0)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify1.0s

Counts
46 → 46
Iterations
IterNodes
done5001
2796
1139
060

prune174.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 0.0625 (pow x 5))
0.6b
(/ 0.125 (* (* x x) x))
15.3b
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
19.6b
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

rewrite851.0ms

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:
6.0ms
(/ 0.0625 (pow x 5))
14.0ms
(/ 0.125 (* (* x x) x))
254.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
526.0ms
(- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5)))

series502.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(/ 0.0625 (pow x 5))
57.0ms
(/ 0.125 (* (* x x) x))
278.0ms
(log (- (- (/ 0.125 (* (* x x) x)) (/ 0.5 x)) (/ 0.0625 (pow x 5))))
94.0ms
(- (- (/ 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

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize18.0ms

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)
0.6b
(/ 0.125 (* (* x x) x))
12.9b
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x))))

rewrite75.0ms

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:
16.0ms
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x)))
17.0ms
(* (* x x) x)
20.0ms
(/ 0.125 (* (* x x) x))
18.0ms
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x))))

series425.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x)))
72.0ms
(* (* x x) x)
51.0ms
(/ 0.125 (* (* x x) x))
237.0ms
(log (- (fma x 2 (/ 0.5 x)) (/ 0.125 (* (* x x) x))))

simplify2.6s

Counts
126 → 126
Iterations
IterNodes
done5000
23401
1529
0213

prune497.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.6b

bsearch133.0ms

Steps
ItersRangePoint
11
3.4817375791661903e-26
573579.0075499975
0.8840407169458702
10
-84463.33967257517
-3.2432757514909933e-09
-0.9983730585657322

simplify5.0ms

Iterations
IterNodes
done35
135
033

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.5s2331×body1280valid
633.0ms1609×body640valid
461.0ms807×body2560valid
168.0ms784×body320valid
138.0ms2084×body80valid
48.0ms385×body160valid