Details

Time bar (total: 14.7s)

sample126.0ms

Algorithm
intervals
Results
58.0ms73×body1280valid
23.0ms51×body640valid
18.0ms34×body2560valid
8.0ms27×body320valid
4.0ms62×body80valid
1.0ms9×body160valid

simplify6.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.1b

localize23.0ms

Local error

Found 3 expressions with local error:

0.8b
(+ x (sqrt (fma x x 1.0)))
2.9b
(log (+ x (sqrt (fma x x 1.0))))
15.4b
(sqrt (fma x x 1.0))

rewrite13.0ms

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:
5.0ms
(+ x (sqrt (fma x x 1.0)))
5.0ms
(log (+ x (sqrt (fma x x 1.0))))
2.0ms
(sqrt (fma x x 1.0))

series430.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(+ x (sqrt (fma x x 1.0)))
263.0ms
(log (+ x (sqrt (fma x x 1.0))))
85.0ms
(sqrt (fma x x 1.0))

simplify1.6s

Counts
58 → 58
Iterations
IterNodes
done5016
32828
2842
1288
0126

prune329.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

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 -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
24.0ms
(* x (* x x))

series180.0ms

Counts
2 → 6
Calls
2 calls:
134.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
46.0ms
(* x (* x x))

simplify1.6s

Counts
42 → 42
Iterations
IterNodes
done5034
31358
2384
1117
061

prune162.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.4b
(/ 0.125 (* x (* x x)))
11.4b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
18.3b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite417.0ms

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))
17.0ms
(/ 0.125 (* x (* x x)))
174.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
215.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ 0.0625 (pow x 5))
54.0ms
(/ 0.125 (* x (* x x)))
236.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
67.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify2.1s

Counts
170 → 170
Iterations
IterNodes
done5012
22870
1761
0320

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.8b
(+ (hypot x (sqrt 1.0)) x)
2.9b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite14.0ms

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))
6.0ms
(+ (hypot x (sqrt 1.0)) x)
7.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series769.0ms

Counts
3 → 9
Calls
3 calls:
158.0ms
(hypot x (sqrt 1.0))
180.0ms
(+ (hypot x (sqrt 1.0)) x)
431.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify1.6s

Counts
53 → 53
Iterations
IterNodes
done5003
32791
2771
1275
0118

prune281.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes71.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.3b

bsearch97.0ms

Steps
ItersRangePoint
8
0.0004390994911134099
0.778402845272117
0.001178095637719532
8
-2980.3304644899954
-0.1501579911863904
-1.01308332610721

simplify10.0ms

Iterations
IterNodes
done37
137
032

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.7s2287×body1280valid
608.0ms1570×body640valid
420.0ms840×body2560valid
152.0ms767×body320valid
132.0ms2109×body80valid
75.0ms427×body160valid