Details

Time bar (total: 7.9s)

sample43.0ms

Algorithm
intervals
Results
10.0ms276×body80nan
9.0ms60×body640valid
5.0ms140×body80valid
5.0ms29×body1280valid
2.0ms19×body320valid
1.0ms8×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0116
1146
2146

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.2b

Counts
2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.3b
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
1035×times-frac
879×*-un-lft-identity
747×add-sqr-sqrt
714×add-cube-cbrt
594×prod-diff
566×sqrt-prod
74×distribute-lft-out
54×div-inv
48×sqrt-div
46×associate-/r/
24×flip3-+ flip-+
22×fma-neg
13×associate-/r*
11×distribute-lft-out--
9×difference-of-squares
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log frac-sub flip-- hypot-def
Counts
4 → 758
Calls
4 calls:
4.0ms
(sqrt (+ x 1.0))
10.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
48.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series288.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
78.0ms
(/ 1.0 (sqrt (+ x 1.0)))
44.0ms
(/ 1.0 (sqrt x))
136.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify267.0ms

Algorithm
egg-herbie
Counts
770 → 770
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
0153825021
1427818390
2500118355

prune1.1s

Filtered
770 candidates to 303 candidates (39.4%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New75416770
Fresh000
Picked101
Done000
Total75516771

Merged error: 17.6b

Counts
771 → 16

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (sqrt x) (sqrt 1.0))
0.1b
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
0.2b
(/ 1.0 (sqrt x))
2.3b
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
490×times-frac
384×add-sqr-sqrt
373×*-un-lft-identity
365×add-cube-cbrt
286×prod-diff
140×sqrt-prod
40×div-inv
22×fma-neg
9×associate-/r*
8×add-exp-log add-cbrt-cube
6×associate-/l* add-log-exp difference-of-squares
5×distribute-lft-out--
4×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num
1×sub-neg hypot-udef flip3-- diff-log frac-sub flip--
Counts
4 → 414
Calls
4 calls:
1.0ms
(hypot (sqrt x) (sqrt 1.0))
3.0ms
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
4.0ms
(/ 1.0 (sqrt x))
31.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
239.0ms
(hypot (sqrt x) (sqrt 1.0))
591.0ms
(/ 1.0 (hypot (sqrt x) (sqrt 1.0)))
39.0ms
(/ 1.0 (sqrt x))
622.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (hypot (sqrt x) (sqrt 1.0))))

simplify177.0ms

Algorithm
egg-herbie
Counts
426 → 426
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
0126213797
139009945
250019914

prune627.0ms

Filtered
426 candidates to 200 candidates (46.9%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New4251426
Fresh21315
Picked011
Done000
Total42715442

Merged error: 17.6b

Counts
442 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (sqrt x))
0.3b
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
0.5b
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
2.3b
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
240×*-un-lft-identity
167×add-sqr-sqrt
125×add-cube-cbrt
120×sqrt-prod
70×distribute-lft-out
28×swap-sqr
22×associate-*r* associate-*l*
20×add-exp-log associate-/r* add-cbrt-cube
18×frac-sub
16×div-inv difference-of-squares
13×frac-times associate-*r/ associate-*l/
11×pow1 associate-/l/
9×unswap-sqr
7×associate-/l*
6×cbrt-undiv div-exp add-log-exp
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u
3×associate-/r/
2×flip3-- frac-2neg clear-num flip--
1×pow2 sub-neg flip3-+ pow-plus fma-neg diff-log div-sub prod-diff pow-prod-down frac-add pow-sqr *-commutative pow-prod-up flip-+
Counts
4 → 277
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt x))
44.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
20.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
11.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(/ 1.0 (sqrt x))
341.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
26.0ms
(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
63.0ms
(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify72.0ms

Algorithm
egg-herbie
Counts
289 → 289
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
012364760
150024431

prune522.0ms

Filtered
289 candidates to 175 candidates (60.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2863289
Fresh9413
Picked101
Done101
Total2977304

Merged error: 4.7b

Counts
304 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (sqrt x))
0.3b
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.9b
(- (+ x 1.0) x)

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
319×*-un-lft-identity
296×times-frac
124×sqrt-prod
121×distribute-lft-out
116×add-sqr-sqrt
114×add-cube-cbrt
37×add-exp-log add-cbrt-cube
35×associate-/r/
34×div-inv
30×associate-*l/
27×associate-/r*
17×flip3-+ flip-+
15×cbrt-undiv div-exp
13×associate-/l*
12×prod-diff
9×prod-exp cbrt-unprod add-log-exp
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
3×frac-2neg clear-num
2×sqrt-div diff-log distribute-lft-out--
1×sub-neg flip3-- frac-add associate--l+ sum-log flip-- associate-/l/ difference-of-squares
Counts
4 → 272
Calls
4 calls:
6.0ms
(/ 1.0 (sqrt (+ x 1.0)))
4.0ms
(/ 1.0 (sqrt x))
54.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
7.0ms
(- (+ x 1.0) x)

series618.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ 1.0 (sqrt (+ x 1.0)))
43.0ms
(/ 1.0 (sqrt x))
495.0ms
(/ (/ (* (* 1.0 1.0) (- (+ x 1.0) x)) (* (+ x 1.0) x)) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
1.0ms
(- (+ x 1.0) x)

simplify71.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013274194
150013759

prune446.0ms

Filtered
284 candidates to 153 candidates (53.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2804284
Fresh426
Picked011
Done000
Total2847291

Merged error: 4.7b

Counts
291 → 7

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 5.9b against oracle of 5.6b and baseline of 5.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01712
11712

end0.0ms

sample1.2s

Algorithm
intervals
Results
298.0ms8187×body80nan
272.0ms1894×body640valid
206.0ms1116×body1280valid
155.0ms4069×body80valid
67.0ms626×body320valid
21.0ms295×body160valid