Details

Time bar (total: 15.1s)

sample95.0ms

Algorithm
intervals
Results
42.0ms69×body1280valid
24.0ms69×body640valid
10.0ms24×body2560valid
4.0ms21×body320valid
3.0ms61×body80valid
1.0ms12×body160valid

simplify3.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.6b

localize17.0ms

Local error

Found 3 expressions with local error:

0.4b
(+ x (sqrt (fma x x 1.0)))
2.1b
(log (+ x (sqrt (fma x x 1.0))))
14.0b
(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))

series478.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(+ x (sqrt (fma x x 1.0)))
280.0ms
(log (+ x (sqrt (fma x x 1.0))))
98.0ms
(sqrt (fma x x 1.0))

simplify1.8s

Counts
58 → 58
Iterations
IterNodes
done5016
32828
2842
1288
0126

prune404.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

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:
19.0ms
(* x (* x x))
0.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series202.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(* x (* x x))
156.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify1.8s

Counts
42 → 42
Iterations
IterNodes
done5027
31508
2384
1119
061

prune249.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.4b
(+ (hypot x (sqrt 1.0)) x)
2.1b
(log (+ (hypot x (sqrt 1.0)) x))

rewrite18.0ms

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))
9.0ms
(+ (hypot x (sqrt 1.0)) x)
7.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series735.0ms

Counts
3 → 9
Calls
3 calls:
129.0ms
(hypot x (sqrt 1.0))
189.0ms
(+ (hypot x (sqrt 1.0)) x)
416.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify1.8s

Counts
53 → 53
Iterations
IterNodes
done5003
32791
2771
1275
0118

prune275.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (* x (* x x)))
11.4b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
21.5b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite478.0ms

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:
13.0ms
(/ 0.0625 (pow x 5))
27.0ms
(/ 0.125 (* x (* x x)))
204.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
222.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series501.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ 0.0625 (pow x 5))
64.0ms
(/ 0.125 (* x (* x x)))
298.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
74.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify2.0s

Counts
170 → 170
Iterations
IterNodes
done5012
22870
1761
0320

prune955.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes55.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.2b

bsearch108.0ms

Steps
ItersRangePoint
9
1.0117869227030548e-08
0.0022991053059264813
0.000987539903020136
10
-733100.9210806559
-4.034181863829644e-08
-1.0212215988225002

simplify5.0ms

Iterations
IterNodes
done37
137
032

end0.0ms

sample3.1s

Algorithm
intervals
Results
1.3s2298×body1280valid
833.0ms1550×body640valid
340.0ms819×body2560valid
232.0ms806×body320valid
160.0ms2136×body80valid
51.0ms391×body160valid