Details

Time bar (total: 14.3s)

sample95.0ms

Algorithm
intervals
Results
39.0ms69×body1280valid
19.0ms51×body640valid
10.0ms20×body2560valid
8.0ms33×body320valid
4.0ms71×body80valid
1.0ms12×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
done10
110
07

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.5b

localize19.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (fma x x 1.0)))
3.1b
(log (+ x (sqrt (fma x x 1.0))))
15.2b
(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))

series452.0ms

Counts
3 → 9
Calls
3 calls:
81.0ms
(+ x (sqrt (fma x x 1.0)))
293.0ms
(log (+ x (sqrt (fma x x 1.0))))
78.0ms
(sqrt (fma x x 1.0))

simplify1.8s

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

localize30.0ms

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))

rewrite18.0ms

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))))
17.0ms
(* x (* x x))

series169.0ms

Counts
2 → 6
Calls
2 calls:
133.0ms
(fma -1/6 (/ (* x (* x x)) (* 1.0 (sqrt 1.0))) (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))
36.0ms
(* x (* x x))

simplify1.7s

Counts
42 → 42
Iterations
IterNodes
done5034
31358
2384
1117
061

prune165.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
8×*-un-lft-identity
4×add-sqr-sqrt log-prod add-cube-cbrt add-log-exp
3×pow1 fma-def add-exp-log
2×expm1-log1p-u log-div flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×+-commutative sum-log rem-log-exp log-pow
Counts
2 → 34
Calls
2 calls:
12.0ms
(+ (hypot x (sqrt 1.0)) x)
7.0ms
(log (+ (hypot x (sqrt 1.0)) x))

series550.0ms

Counts
2 → 6
Calls
2 calls:
166.0ms
(+ (hypot x (sqrt 1.0)) x)
383.0ms
(log (+ (hypot x (sqrt 1.0)) x))

simplify1.4s

Counts
40 → 40
Iterations
IterNodes
done5000
32558
2729
1243
0102

prune150.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 0.125 (* x (* x x)))
0.3b
(/ 0.0625 (pow x 5))
11.7b
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
17.1b
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

rewrite404.0ms

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:
22.0ms
(/ 0.125 (* x (* x x)))
9.0ms
(/ 0.0625 (pow x 5))
174.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
191.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

series471.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 0.125 (* x (* x x)))
74.0ms
(/ 0.0625 (pow x 5))
252.0ms
(log (- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x))))
92.0ms
(- (/ 0.125 (* x (* x x))) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))

simplify1.9s

Counts
170 → 170
Iterations
IterNodes
done5002
22882
1765
0320

prune764.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes36.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 32.1b

bsearch108.0ms

Steps
ItersRangePoint
11
1.9534460235190362e-22
53640.016154094046
0.0010835521119949194
10
-17239113253358.373
-4.96108325192681e-05
-1.0098163723001696

simplify5.0ms

Iterations
IterNodes
done37
137
032

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.9s2408×body1280valid
652.0ms1473×body640valid
457.0ms786×body2560valid
235.0ms808×body320valid
110.0ms2122×body80valid
50.0ms403×body160valid