Details

Time bar (total: 4.5s)

sample18.0ms

Algorithm
intervals
Results
8.0ms272×body80valid

simplify18.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 5.6b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

3.4b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b
(* y (+ 1.0 (* z z)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
20×add-sqr-sqrt
18×add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
4×pow1 associate-*r/
3×associate-*r* associate-*l* prod-exp cbrt-unprod div-inv
2×flip3-+ associate-/r/ flip-+ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* *-commutative associate-/l/ unswap-sqr
Counts
2 → 70
Calls
2 calls:
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
6.0ms
(* y (+ 1.0 (* z z)))

series131.0ms

Counts
2 → 6
Calls
2 calls:
67.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
63.0ms
(* y (+ 1.0 (* z z)))

simplify62.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0409511
11963443
25001443

prune206.0ms

Filtered
76 candidates to 56 candidates (73.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New661076
Fresh000
Picked101
Done000
Total671077

Merged error: 3.1b

Counts
77 → 10

localize10.0ms

Local error

Found 2 expressions with local error:

2.9b
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
3.4b
(/ (/ 1.0 x) (+ 1.0 (* z z)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
116×add-sqr-sqrt
89×*-un-lft-identity
86×add-cube-cbrt
46×add-exp-log
45×associate-*r*
28×add-cbrt-cube
21×div-exp
13×associate-*l* associate-/l*
12×cbrt-undiv prod-exp
10×div-inv
9×unswap-sqr
6×cbrt-unprod
4×pow1 associate-/r/
3×rec-exp 1-exp associate-/r*
2×flip3-+ flip-+ add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
2 → 169
Calls
2 calls:
24.0ms
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
8.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

series154.0ms

Counts
2 → 6
Calls
2 calls:
77.0ms
(* (/ 1 y) (/ (/ 1.0 x) (+ 1.0 (* z z))))
77.0ms
(/ (/ 1.0 x) (+ 1.0 (* z z)))

simplify124.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (105.0ms)

IterNodesCost
09221637
145381473
250031467

prune669.0ms

Filtered
175 candidates to 133 candidates (76.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1723175
Fresh279
Picked101
Done000
Total17510185

Merged error: 3.1b

Counts
185 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
2.3b
(/ (/ 1 y) (* (sqrt (+ 1.0 (* z z))) (* (cbrt x) (cbrt x))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
43×add-exp-log
31×times-frac
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity add-cbrt-cube
18×div-exp
13×associate-/l*
12×prod-exp
9×cbrt-undiv
6×pow1 sqrt-div sqrt-prod cbrt-unprod
4×add-log-exp
3×cbrt-prod rec-exp flip3-+ 1-exp flip-+ div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ associate-/r/
1×frac-2neg pow1/3 clear-num associate-/r* associate-/l/
Counts
4 → 99
Calls
4 calls:
1.0ms
(cbrt x)
16.0ms
(/ (/ 1 y) (* (sqrt (+ 1.0 (* z z))) (* (cbrt x) (cbrt x))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series526.0ms

Counts
4 → 12
Calls
4 calls:
201.0ms
(cbrt x)
228.0ms
(/ (/ 1 y) (* (sqrt (+ 1.0 (* z z))) (* (cbrt x) (cbrt x))))
44.0ms
(sqrt (+ 1.0 (* z z)))
53.0ms
(sqrt (+ 1.0 (* z z)))

simplify87.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
0589992
12553825
25002780

prune323.0ms

Filtered
111 candidates to 74 candidates (66.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1101111
Fresh099
Picked101
Done000
Total11110121

Merged error: 3.1b

Counts
121 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1 y))
1.5b
(* (/ (* (cbrt (/ 1 y)) (cbrt (/ 1 y))) (sqrt (+ 1.0 (* z z)))) (/ (cbrt (/ 1 y)) (* (cbrt x) (cbrt x))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
68×times-frac
60×add-sqr-sqrt
40×add-exp-log
35×cbrt-prod
28×*-un-lft-identity
25×add-cube-cbrt
22×add-cbrt-cube
20×associate-*r*
15×prod-exp cbrt-unprod unswap-sqr
14×sqrt-prod
12×cbrt-undiv div-exp associate-*l*
8×pow1
6×sqrt-div
4×div-inv add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×frac-times cbrt-div pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 129
Calls
4 calls:
3.0ms
(cbrt (/ 1 y))
27.0ms
(* (/ (* (cbrt (/ 1 y)) (cbrt (/ 1 y))) (sqrt (+ 1.0 (* z z)))) (/ (cbrt (/ 1 y)) (* (cbrt x) (cbrt x))))
3.0ms
(sqrt (+ 1.0 (* z z)))
7.0ms
(sqrt (+ 1.0 (* z z)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(cbrt (/ 1 y))
157.0ms
(* (/ (* (cbrt (/ 1 y)) (cbrt (/ 1 y))) (sqrt (+ 1.0 (* z z)))) (/ (cbrt (/ 1 y)) (* (cbrt x) (cbrt x))))
56.0ms
(sqrt (+ 1.0 (* z z)))
50.0ms
(sqrt (+ 1.0 (* z z)))

simplify110.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06941975
132791664
250011539

prune468.0ms

Filtered
141 candidates to 100 candidates (70.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1410141
Fresh099
Picked011
Done000
Total14110151

Merged error: 3.1b

Counts
151 → 10

regimes363.0ms

Accuracy

37.9% (0.7b remaining)

Error of 5.4b against oracle of 4.7b and baseline of 5.8b

bsearch96.0ms

Steps
ItersRangePoint
8
1.574168358726979e+256
4.895518686476394e+258
1.5982897855907784e+256
8
-51330663.2772825
-45386.90934105675
-64215.42507143619

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02811
12811

end0.0ms

sample462.0ms

Algorithm
intervals
Results
277.0ms8648×body80valid