Details

Time bar (total: 14.8s)

sample17.0ms

Algorithm
intervals
Results
7.0ms273×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

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: 7.4b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.8b
(* y (+ 1.0 (* z z)))
4.6b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
317×times-frac
213×*-un-lft-identity
183×add-sqr-sqrt
153×add-cube-cbrt
75×associate-*r*
60×associate-*l*
30×distribute-lft-out
17×associate-/r*
16×add-exp-log add-cbrt-cube div-inv associate-/l*
15×*-commutative unswap-sqr
9×associate-/l/
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×prod-exp cbrt-unprod
2×+-commutative distribute-rgt-in frac-2neg distribute-lft-in flip3-+ clear-num associate-/r/ flip-+ add-log-exp
1×pow-prod-down
Counts
2 → 264
Calls
2 calls:
9.0ms
(* y (+ 1.0 (* z z)))
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series121.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(* y (+ 1.0 (* z z)))
63.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify123.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011052749
148612670
250012670

prune397.0ms

Filtered
270 candidates to 178 candidates (65.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2628270
Fresh000
Picked101
Done000
Total2638271

Merged error: 5.3b

Counts
271 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
1.2b
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
16.1b
(sqrt (+ 1.0 (* z z)))
16.1b
(sqrt (+ 1.0 (* z z)))

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
934×*-un-lft-identity
905×associate-/r*
889×add-sqr-sqrt
792×frac-times
600×add-cube-cbrt
570×times-frac
508×associate-/l*
465×sqrt-prod
438×associate-*r*
264×associate-*l*
228×associate-/l/
162×distribute-lft-out
124×unswap-sqr
87×clear-num
85×frac-2neg
69×add-exp-log
45×add-cbrt-cube
42×*-commutative
37×associate-*r/ div-inv
30×div-exp
24×associate-*l/
21×prod-exp
17×cbrt-undiv
13×cbrt-unprod
10×sqrt-div
8×pow1
6×associate-/r/ un-div-inv
5×flip3-+ flip-+
4×add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-prod-down
Counts
4 → 1211
Calls
4 calls:
17.0ms
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
133.0ms
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
6.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series253.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ 1.0 (* y (sqrt (+ 1.0 (* z z)))))
72.0ms
(* (/ 1.0 (* y (sqrt (+ 1.0 (* z z))))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
46.0ms
(sqrt (+ 1.0 (* z z)))
54.0ms
(sqrt (+ 1.0 (* z z)))

simplify257.0ms

Algorithm
egg-herbie
Counts
1223 → 1223
Iterations

Useful iterations: 1 (90.0ms)

IterNodesCost
0423116165
1500215016

prune1.6s

Filtered
1223 candidates to 503 candidates (41.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New122031223
Fresh437
Picked011
Done000
Total122471231

Merged error: 5.3b

Counts
1231 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

1.5b
(* (/ 1 (* (cbrt x) (cbrt x))) (/ (/ 1.0 y) (fabs (cbrt (+ 1.0 (* z z))))))
16.1b
(sqrt (+ 1.0 (* z z)))
16.7b
(cbrt (+ 1.0 (* z z)))
16.7b
(cbrt (+ 1.0 (* z z)))

rewrite220.0ms

Algorithm
rewrite-expression-head
Rules
1206×add-sqr-sqrt
987×associate-/r*
924×frac-times
768×*-un-lft-identity
727×add-cube-cbrt
633×associate-/l*
564×times-frac
558×cbrt-prod
308×associate-/l/
280×associate-*l*
235×associate-*r*
209×unswap-sqr
204×swap-sqr
99×clear-num
97×frac-2neg
82×add-exp-log
73×add-cbrt-cube
39×*-commutative div-inv
33×cbrt-undiv div-exp associate-*l/
30×prod-exp cbrt-unprod
28×associate-*r/
7×pow1
6×rec-exp 1-exp distribute-lft-out
5×sqrt-prod
4×cbrt-div un-div-inv add-log-exp
3×flip3-+ flip-+
2×pow1/3 sqrt-div
1×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down
Counts
4 → 1269
Calls
4 calls:
96.0ms
(* (/ 1 (* (cbrt x) (cbrt x))) (/ (/ 1.0 y) (fabs (cbrt (+ 1.0 (* z z))))))
6.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(cbrt (+ 1.0 (* z z)))
6.0ms
(cbrt (+ 1.0 (* z z)))

series568.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(* (/ 1 (* (cbrt x) (cbrt x))) (/ (/ 1.0 y) (fabs (cbrt (+ 1.0 (* z z))))))
50.0ms
(sqrt (+ 1.0 (* z z)))
182.0ms
(cbrt (+ 1.0 (* z z)))
183.0ms
(cbrt (+ 1.0 (* z z)))

simplify233.0ms

Algorithm
egg-herbie
Counts
1281 → 1281
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500120472

prune3.5s

Filtered
1281 candidates to 761 candidates (59.4%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New128101281
Fresh055
Picked011
Done011
Total128171288

Merged error: 5.3b

Counts
1288 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) y))
2.8b
(/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) y)
16.1b
(sqrt (+ 1.0 (* z z)))
16.1b
(sqrt (+ 1.0 (* z z)))

rewrite866.0ms

Algorithm
rewrite-expression-head
Rules
4779×times-frac
4553×*-un-lft-identity
2839×add-sqr-sqrt
2710×add-cube-cbrt
2469×associate-/l*
2307×sqrt-prod
2086×frac-times
1424×associate-/r*
914×distribute-lft-out
678×associate-/l/
487×associate-*l*
334×associate-*r*
217×div-inv
201×clear-num
198×frac-2neg
149×associate-*r/
73×add-exp-log
50×sqrt-div
46×associate-/r/
45×add-cbrt-cube
38×div-exp
30×unswap-sqr
25×flip3-+ flip-+
22×cbrt-undiv
16×prod-exp
14×associate-*l/
8×pow1 cbrt-unprod
6×un-div-inv
4×rec-exp 1-exp add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×pow-prod-down *-commutative
Counts
4 → 3208
Calls
4 calls:
252.0ms
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) y))
37.0ms
(/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) y)
6.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series261.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (/ 1 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) y))
91.0ms
(/ (/ (/ 1.0 x) (sqrt (+ 1.0 (* z z)))) y)
50.0ms
(sqrt (+ 1.0 (* z z)))
54.0ms
(sqrt (+ 1.0 (* z z)))

simplify584.0ms

Algorithm
egg-herbie
Counts
3220 → 3220
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
0500158825

prune4.8s

Filtered
3220 candidates to 1442 candidates (44.8%)
Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New321913220
Fresh134
Picked011
Done022
Total322073227

Merged error: 5.3b

Counts
3227 → 7

regimes206.0ms

Accuracy

0% (1.3b remaining)

Error of 6.2b against oracle of 4.9b and baseline of 6.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02622
12622

end0.0ms

sample442.0ms

Algorithm
intervals
Results
253.0ms8659×body80valid