Details

Time bar (total: 5.3s)

sample17.0ms

Algorithm
intervals
Results
8.0ms271×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 4.9b

Counts
2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* z z))
3.4b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.2b
(* y (+ 1.0 (* z z)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
17×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
5×pow1 add-log-exp
4×associate-*r/
3×expm1-log1p-u fma-def flip3-+ associate-*r* associate-*l* prod-exp cbrt-unprod flip-+ log1p-expm1-u div-inv
2×associate-/r/
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* sum-log *-commutative associate-/l/ unswap-sqr
Counts
3 → 90
Calls
3 calls:
3.0ms
(+ 1.0 (* z z))
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.0ms
(* y (+ 1.0 (* z z)))

series146.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ 1.0 (* z z))
62.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
52.0ms
(* y (+ 1.0 (* z z)))

simplify54.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0443593
12151472
25001463

prune227.0ms

Filtered
99 candidates to 78 candidates (78.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New93699
Fresh011
Picked011
Done000
Total938101

Merged error: 4.8b

Counts
101 → 8

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* z z))
0.2b
(/ (/ 1.0 y) x)
5.6b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
230×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
17×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
5×add-log-exp
3×pow1 expm1-log1p-u fma-def log1p-expm1-u
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ associate-/l/
1×+-commutative sum-log
Counts
3 → 284
Calls
3 calls:
3.0ms
(+ 1.0 (* z z))
9.0ms
(/ (/ 1.0 y) x)
13.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series110.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ 1.0 (* z z))
25.0ms
(/ (/ 1.0 y) x)
54.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify109.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
011653074
147892900
250012900

prune779.0ms

Filtered
293 candidates to 254 candidates (86.7%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New2912293
Fresh336
Picked011
Done101
Total2956301

Merged error: 4.8b

Counts
301 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
3.1b
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite211.0ms

Algorithm
rewrite-expression-head
Rules
1464×times-frac
773×add-sqr-sqrt
655×*-un-lft-identity
649×add-cube-cbrt
297×sqrt-prod
264×associate-*r*
69×add-exp-log
55×div-inv
45×add-cbrt-cube
43×associate-/l*
39×div-exp
27×unswap-sqr
24×associate-*l*
22×cbrt-undiv
12×prod-exp
10×sqrt-div
8×pow1 cbrt-unprod
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 715
Calls
4 calls:
114.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
28.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series412.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
260.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
41.0ms
(sqrt (+ 1.0 (* z z)))
51.0ms
(sqrt (+ 1.0 (* z z)))

simplify138.0ms

Algorithm
egg-herbie
Counts
727 → 727
Iterations

Useful iterations: 1 (45.0ms)

IterNodesCost
0276310745
1500210192

prune1.5s

Filtered
727 candidates to 393 candidates (54.1%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New7252727
Fresh224
Picked011
Done011
Total7276733

Merged error: 4.8b

Counts
733 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(* (* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 y) (sqrt (sqrt (+ 1.0 (* z z)))))) (/ (/ 1 x) (sqrt (sqrt (+ 1.0 (* z z))))))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
294×add-exp-log
198×times-frac
151×div-exp
126×sqrt-prod
123×associate-*r*
116×add-sqr-sqrt
112×add-cbrt-cube
110×add-cube-cbrt *-un-lft-identity
105×prod-exp
48×cbrt-undiv
39×cbrt-unprod
21×rec-exp 1-exp
12×pow1
10×sqrt-div div-inv
5×frac-times associate-*l/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down hypot-def
2×associate-/r/
1×associate-*l* *-commutative
Counts
4 → 273
Calls
4 calls:
47.0ms
(* (* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 y) (sqrt (sqrt (+ 1.0 (* z z)))))) (/ (/ 1 x) (sqrt (sqrt (+ 1.0 (* z z))))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series203.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* (* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ 1 y) (sqrt (sqrt (+ 1.0 (* z z)))))) (/ (/ 1 x) (sqrt (sqrt (+ 1.0 (* z z))))))
48.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))
49.0ms
(sqrt (+ 1.0 (* z z)))

simplify72.0ms

Algorithm
egg-herbie
Counts
285 → 285
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
016145185
150014477

prune565.0ms

Filtered
285 candidates to 134 candidates (47.0%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New2850285
Fresh033
Picked011
Done022
Total2856291

Merged error: 4.8b

Counts
291 → 6

regimes144.0ms

Accuracy

0% (1.8b remaining)

Error of 6.8b against oracle of 5.1b and baseline of 6.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01711
11711

end0.0ms

sample441.0ms

Algorithm
intervals
Results
256.0ms8683×body80valid