Details

Time bar (total: 7.1s)

sample13.0ms

Algorithm
intervals
Results
6.0ms256×body80valid

simplify2.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
057
167
done67

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize6.0ms

Local error

Found 1 expressions with local error:

15.0b
(/ x (+ (* x x) 1.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
3×associate-/r* add-cbrt-cube add-exp-log associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv clear-num frac-2neg flip3-+ div-exp flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
11.0ms
(/ x (+ (* x x) 1.0))

series108.0ms

Counts
1 → 3
Calls
1 calls:
108.0ms
(/ x (+ (* x x) 1.0))

simplify1.1s

Counts
32 → 32
Iterations

Useful iterations: done (1.1s)

IterNodesCost
074428
1183415
2783377
done5000375

prune119.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b
(/ x (sqrt (+ (* x x) 1.0)))
15.0b
(sqrt (+ (* x x) 1.0))
15.0b
(sqrt (+ (* x x) 1.0))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×*-un-lft-identity times-frac add-cube-cbrt
30×sqrt-prod
12×associate-/r*
10×add-exp-log
8×pow1 add-cbrt-cube sqrt-div
6×associate-/l*
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×sqrt-pow1 pow1/2 div-exp pow-flip
2×cbrt-undiv rem-sqrt-square clear-num frac-2neg div-inv
1×rec-exp 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
21.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
12.0ms
(/ x (sqrt (+ (* x x) 1.0)))
8.0ms
(sqrt (+ (* x x) 1.0))
8.0ms
(sqrt (+ (* x x) 1.0))

series455.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
191.0ms
(/ x (sqrt (+ (* x x) 1.0)))
60.0ms
(sqrt (+ (* x x) 1.0))
83.0ms
(sqrt (+ (* x x) 1.0))

simplify888.0ms

Counts
130 → 130
Iterations

Useful iterations: 2 (321.0ms)

IterNodesCost
01871855
14171634
219931522
done50001522

prune825.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
0.1b
(/ 1.0 (pow x 3))
0.3b
(/ 1.0 (pow x 5))
20.1b
(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

rewrite422.0ms

Algorithm
rewrite-expression-head
Rules
109×add-sqr-sqrt
97×times-frac
69×*-un-lft-identity
47×add-cube-cbrt
33×unpow-prod-down
20×difference-of-squares
19×associate-/r*
17×sqr-pow
16×cube-prod
14×add-exp-log
11×add-log-exp
8×add-cbrt-cube distribute-lft-out--
6×div-exp div-inv associate-/l*
5×distribute-lft-out
4×cube-mult pow1 unpow3
3×frac-add
2×pow-to-exp cbrt-undiv associate-+r+ clear-num sum-log sub-neg frac-2neg flip3-- diff-log pow-exp frac-sub flip--
1×+-commutative associate-+r- flip3-+ flip-+
Counts
4 → 171
Calls
4 calls:
250.0ms
(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
14.0ms
(/ 1.0 (pow x 3))
11.0ms
(/ 1.0 (pow x 5))
135.0ms
(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(+ (/ 1 x) (- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3))))
75.0ms
(/ 1.0 (pow x 3))
97.0ms
(/ 1.0 (pow x 5))
213.0ms
(- (/ 1.0 (pow x 5)) (/ 1.0 (pow x 3)))

simplify1.3s

Counts
183 → 183
Iterations

Useful iterations: 2 (659.0ms)

IterNodesCost
02572827
15982514
228172450
done50002450

prune611.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes99.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 14.5b

bsearch45.0ms

Steps
ItersRangePoint
7
13.800596953327334
2205.5689030668646
507.01009039307485
2
-3.2275392569223236e+62
-2.967245708633018e+62
-3.1950025633861604e+62

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
02145
12831
done2831

end0.0ms

sample545.0ms

Algorithm
intervals
Results
344.0ms8000×body80valid