Details

Time bar (total: 14.7s)

sample149.0ms

Algorithm
intervals
Results
68.0ms83×body1280valid
27.0ms26×body2560valid
22.0ms46×body640valid
8.0ms26×body320valid
5.0ms61×body80valid
3.0ms14×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize26.0ms

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))

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)))
9.0ms
(log (+ x (sqrt (fma x x 1.0))))
3.0ms
(sqrt (fma x x 1.0))

series460.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(+ x (sqrt (fma x x 1.0)))
268.0ms
(log (+ x (sqrt (fma x x 1.0))))
111.0ms
(sqrt (fma x x 1.0))

simplify1.9s

Counts
58 → 58
Iterations
IterNodes
done5016
32828
2842
1288
0126

prune343.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

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:
13.0ms
(* x (* x x))
0.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series213.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(* x (* x x))
156.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify1.6s

Counts
42 → 42
Iterations
IterNodes
done5027
31508
2384
1119
061

prune158.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize23.0ms

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))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
19.6b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite390.0ms

Algorithm
rewrite-expression-head
Rules
94×*-un-lft-identity
56×times-frac
46×add-sqr-sqrt
42×add-cube-cbrt
35×prod-diff
19×add-exp-log
16×distribute-lft-out
15×add-cbrt-cube
12×unpow-prod-down
9×add-log-exp
8×associate-/r* div-inv
7×fma-neg
6×log-prod div-exp frac-sub associate-/l*
5×pow1 log-div
4×expm1-log1p-u cbrt-undiv log1p-expm1-u distribute-lft-out-- sqr-pow
3×prod-exp cbrt-unprod
2×clear-num frac-2neg flip3-+ flip3-- diff-log frac-add flip-+ flip-- difference-of-squares
1×pow-to-exp sum-log sub-neg rem-log-exp pow-exp log-pow associate--r+
Counts
4 → 158
Calls
4 calls:
6.0ms
(/ 0.0625 (pow x 5))
14.0ms
(/ 0.125 (* x (* x x)))
170.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
193.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 0.0625 (pow x 5))
54.0ms
(/ 0.125 (* x (* x x)))
227.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
71.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.9s

Counts
170 → 170
Iterations
IterNodes
done5012
22870
1761
0320

prune844.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.6b
(+ (hypot x (sqrt 1.0)) x)
3.1b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef sum-log rem-log-exp log-pow
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
5.0ms
(+ (hypot x (sqrt 1.0)) x)
4.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series651.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(hypot x (sqrt 1.0))
148.0ms
(+ (hypot x (sqrt 1.0)) x)
385.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify1.4s

Counts
53 → 53
Iterations
IterNodes
done5003
32791
2771
1275
0118

prune261.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.6b

bsearch125.0ms

Steps
ItersRangePoint
11
3.4817375791661903e-26
573579.0075499975
0.0005269995288876961
10
-84463.33967257517
-3.2432757514909933e-09
-0.9983730585657322

simplify6.0ms

Iterations
IterNodes
done37
137
032

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.0s2331×body1280valid
705.0ms1609×body640valid
394.0ms807×body2560valid
190.0ms784×body320valid
107.0ms2084×body80valid
49.0ms385×body160valid