Details

Time bar (total: 9.5s)

sample16.0ms

Algorithm
intervals
Results
7.0ms271×body80valid

simplify15.0ms

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

localize7.0ms

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)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
317×times-frac
219×*-un-lft-identity
185×add-sqr-sqrt
155×add-cube-cbrt
75×associate-*r*
61×associate-*l*
32×distribute-lft-out
17×add-exp-log associate-/r* add-cbrt-cube
16×div-inv associate-/l*
15×*-commutative unswap-sqr
9×associate-/l/
6×cbrt-undiv div-exp
5×pow1 add-log-exp
4×associate-*r/
3×+-commutative expm1-log1p-u fma-def flip3-+ prod-exp cbrt-unprod flip-+ log1p-expm1-u
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r/
1×pow-prod-down sum-log
Counts
3 → 286
Calls
3 calls:
7.0ms
(+ 1.0 (* z z))
22.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
9.0ms
(* y (+ 1.0 (* z z)))

series148.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(+ 1.0 (* z z))
55.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
57.0ms
(* y (+ 1.0 (* z z)))

simplify61.0ms

Algorithm
egg-herbie
Counts
295 → 295
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
011422835
150012588

prune640.0ms

Filtered
295 candidates to 202 candidates (68.5%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2869295
Fresh011
Picked101
Done000
Total28710297

Merged error: 4.8b

Counts
297 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* z z))
0.4b
(/ 1.0 (* y x))
5.6b
(/ (/ 1.0 (* y x)) (+ 1.0 (* z z)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
452×times-frac
374×*-un-lft-identity
252×add-sqr-sqrt
206×add-cube-cbrt
111×associate-*l*
84×distribute-lft-out
69×associate-*r*
46×associate-/l*
29×associate-/r*
23×*-commutative unswap-sqr
18×associate-/l/
17×add-exp-log add-cbrt-cube
8×div-inv
7×cbrt-undiv div-exp
5×add-log-exp
3×pow1 expm1-log1p-u fma-def frac-2neg clear-num log1p-expm1-u
2×flip3-+ prod-exp associate-/r/ cbrt-unprod flip-+
1×+-commutative sum-log
Counts
3 → 368
Calls
3 calls:
7.0ms
(+ 1.0 (* z z))
10.0ms
(/ 1.0 (* y x))
22.0ms
(/ (/ 1.0 (* y x)) (+ 1.0 (* z z)))

series113.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ 1.0 (* z z))
19.0ms
(/ 1.0 (* y x))
62.0ms
(/ (/ 1.0 (* y x)) (+ 1.0 (* z z)))

simplify138.0ms

Algorithm
egg-herbie
Counts
377 → 377
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
010503417
146963168
250013168

prune736.0ms

Filtered
377 candidates to 237 candidates (62.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New3734377
Fresh639
Picked101
Done000
Total3807387

Merged error: 4.8b

Counts
387 → 7

localize11.0ms

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)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
695×times-frac
492×*-un-lft-identity
312×add-sqr-sqrt add-cube-cbrt
90×distribute-lft-out
75×associate-/l*
46×associate-/l/
45×associate-*l*
31×div-inv
17×add-exp-log associate-/r* add-cbrt-cube
9×cbrt-undiv div-exp
5×frac-2neg clear-num add-log-exp
3×pow1 expm1-log1p-u fma-def log1p-expm1-u
2×flip3-+ associate-/r/ flip-+
1×+-commutative sum-log
Counts
3 → 409
Calls
3 calls:
7.0ms
(+ 1.0 (* z z))
7.0ms
(/ (/ 1.0 y) x)
24.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series114.0ms

Counts
3 → 9
Calls
3 calls:
38.0ms
(+ 1.0 (* z z))
19.0ms
(/ (/ 1.0 y) x)
56.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify72.0ms

Algorithm
egg-herbie
Counts
418 → 418
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012454215
150013927

prune913.0ms

Filtered
418 candidates to 281 candidates (67.2%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4153418
Fresh426
Picked011
Done000
Total4196425

Merged error: 4.8b

Counts
425 → 6

localize11.0ms

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)))

rewrite509.0ms

Algorithm
rewrite-expression-head
Rules
3040×times-frac
2524×*-un-lft-identity
1897×add-sqr-sqrt
1755×add-cube-cbrt
1197×associate-/l*
1148×frac-times
971×sqrt-prod
888×associate-/r*
601×associate-/l/
380×distribute-lft-out
350×associate-*r*
220×associate-*l*
148×div-inv
134×clear-num
131×frac-2neg
82×associate-*r/
69×add-exp-log
45×add-cbrt-cube
39×div-exp
29×unswap-sqr
22×cbrt-undiv
14×associate-*l/
12×prod-exp
10×sqrt-div hypot-def
8×pow1 un-div-inv cbrt-unprod
6×associate-/r/
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp *-commutative
2×rem-sqrt-square sqrt-pow1 pow1/2 swap-sqr
1×pow-prod-down
Counts
4 → 2183
Calls
4 calls:
237.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
27.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
8.0ms
(sqrt (+ 1.0 (* z z)))
7.0ms
(sqrt (+ 1.0 (* z z)))

series234.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
74.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
42.0ms
(sqrt (+ 1.0 (* z z)))
53.0ms
(sqrt (+ 1.0 (* z z)))

simplify349.0ms

Algorithm
egg-herbie
Counts
2195 → 2195
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500131454

prune4.7s

Filtered
2195 candidates to 1173 candidates (53.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New219322195
Fresh224
Picked011
Done011
Total219562201

Merged error: 4.8b

Counts
2201 → 6

regimes151.0ms

Accuracy

0% (1.7b 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

sample426.0ms

Algorithm
intervals
Results
254.0ms8683×body80valid