Details

Time bar (total: 1.5s)

sample13.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results
6.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.5b

Counts
2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

15.5b
(/ x (+ (* x x) 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
2×associate-/r/
1×pow1 cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+ div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
8.0ms
(/ x (+ (* x x) 1.0))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(/ x (+ (* x x) 1.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0165210
1555195
21825192
35001192

prune52.0ms

Filtered
26 candidates to 32 candidates (-23.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New29332
Fresh000
Picked101
Done000
Total30333

Merged error: 0b

Counts
33 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
15.5b
(sqrt (+ (* x x) 1.0))
15.5b
(sqrt (+ (* x x) 1.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
30×add-exp-log
24×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
10×pow1 sqrt-div div-exp
8×prod-exp
6×associate-/r* associate-/r/
5×cbrt-undiv flip3-+ flip-+
4×cbrt-unprod add-log-exp
3×rec-exp pow-flip sqrt-pow1 pow1/2 1-exp div-inv associate-/l*
2×rem-sqrt-square
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative inv-pow
Counts
4 → 164
Calls
4 calls:
6.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
22.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series20.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
7.0ms
(* (/ 1 (sqrt (+ (* x x) 1.0))) (/ x (sqrt (+ (* x x) 1.0))))
3.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify74.0ms

Algorithm
egg-herbie
Counts
176 → 176
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06251745
131241542
250021410

prune216.0ms

Filtered
105 candidates to 176 candidates (-67.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1760176
Fresh022
Picked011
Done000
Total1763179

Merged error: 0b

Counts
179 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ 1 (+ (* x x) 1.0))
15.3b
(* x (/ 1 (+ (* x x) 1.0)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
20×times-frac
19×*-un-lft-identity
18×add-cube-cbrt
15×add-exp-log associate-*r*
9×add-cbrt-cube
5×pow1
4×div-exp prod-exp associate-/r/
3×associate-*l* associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ div-inv add-log-exp
1×pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
2 → 71
Calls
2 calls:
5.0ms
(/ 1 (+ (* x x) 1.0))
9.0ms
(* x (/ 1 (+ (* x x) 1.0)))

series8.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(/ 1 (+ (* x x) 1.0))
5.0ms
(* x (/ 1 (+ (* x x) 1.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0316468
11443408
25001372

prune68.0ms

Filtered
47 candidates to 77 candidates (-63.8%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New77077
Fresh011
Picked011
Done011
Total77380

Merged error: 0b

Counts
80 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
0.1b
(/ 1 (pow x 3))
0.3b
(/ 1 (pow x 5))
19.0b
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
196×add-sqr-sqrt
173×times-frac
112×*-un-lft-identity
63×difference-of-squares
56×unpow-prod-down
47×add-cube-cbrt
40×sqr-pow
26×cube-prod
22×add-exp-log
19×associate-/r*
12×div-exp
8×add-cbrt-cube add-log-exp
7×distribute-lft-out--
6×pow-to-exp rec-exp 1-exp pow-exp div-inv associate-/l*
4×pow1 cube-mult associate-+l+ unpow3
3×sub-neg associate-*r/ frac-add
2×cbrt-undiv distribute-rgt-in flip3-- pow-flip frac-2neg distribute-lft-in clear-num frac-sub flip-- inv-pow
1×+-commutative flip3-+ diff-log sum-log flip-+
Counts
4 → 227
Calls
4 calls:
50.0ms
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
5.0ms
(/ 1 (pow x 3))
5.0ms
(/ 1 (pow x 5))
43.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

series23.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* 1.0 (- (/ 1 (pow x 5)) (/ 1 (pow x 3)))) (/ 1 x))
3.0ms
(/ 1 (pow x 3))
4.0ms
(/ 1 (pow x 5))
12.0ms
(- (/ 1 (pow x 5)) (/ 1 (pow x 3)))

simplify87.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06871905
128791620
250011619

prune213.0ms

Filtered
92 candidates to 239 candidates (-159.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New2390239
Fresh000
Picked011
Done022
Total2393242

Merged error: 0b

Counts
242 → 3

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.7b

bsearch42.0ms

Steps
ItersRangePoint
9
0.09821310020651784
8418.71528787905
436.4009909622486
8
-2.145264512850146e+20
-5.318775759870495e+17
-3.2222033842799423e+19

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03212
13212

end0.0ms

sample308.0ms

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results
180.0ms8000×body80valid

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