Details

Time bar (total: 4.9s)

sample18.0ms

Algorithm
intervals
Results
9.0ms274×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.3b

localize7.0ms

Local error

Found 2 expressions with local error:

3.8b
(* y (+ 1.0 (* z z)))
4.7b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite17.0ms

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×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u 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 → 74
Calls
2 calls:
7.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series108.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(* y (+ 1.0 (* z z)))
58.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify47.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0416531
12028428
25001420

prune190.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
6.1b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
468×times-frac
228×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
22×div-inv
16×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×associate-/r*
2×pow1 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 268
Calls
2 calls:
9.0ms
(/ (/ 1.0 y) x)
17.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series80.0ms

Counts
2 → 6
Calls
2 calls:
24.0ms
(/ (/ 1.0 y) x)
56.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify104.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
011383012
145962854
250022850

prune760.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
1.3b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
16.4b
(sqrt (+ 1.0 (* z z)))
16.4b
(sqrt (+ 1.0 (* z z)))

rewrite178.0ms

Algorithm
rewrite-expression-head
Rules
497×times-frac
377×add-sqr-sqrt
231×*-un-lft-identity
221×add-cube-cbrt
155×sqrt-prod
84×associate-*r* associate-*l*
73×add-exp-log
45×add-cbrt-cube
39×div-exp
35×unswap-sqr
22×div-inv
21×cbrt-undiv
15×prod-exp
13×associate-/l*
10×sqrt-div
9×cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-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 → 395
Calls
4 calls:
9.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
139.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
64.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
50.0ms
(sqrt (+ 1.0 (* z z)))
50.0ms
(sqrt (+ 1.0 (* z z)))

simplify86.0ms

Algorithm
egg-herbie
Counts
407 → 407
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015845456
150025076

prune882.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
1.5b
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (* (sqrt (+ 1.0 (* z z))) x))
16.4b
(sqrt (+ 1.0 (* z z)))
16.4b
(sqrt (+ 1.0 (* z z)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
489×times-frac
225×add-sqr-sqrt
221×add-cube-cbrt *-un-lft-identity
126×sqrt-prod
97×associate-/l*
30×add-exp-log add-cbrt-cube
23×div-inv
15×cbrt-undiv div-exp
12×sqrt-div
8×associate-/r/
7×associate-/r*
6×pow1 flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×prod-exp cbrt-unprod
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*l/ clear-num hypot-def associate-/l/
Counts
4 → 348
Calls
4 calls:
9.0ms
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
32.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (* (sqrt (+ 1.0 (* z z))) x))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
72.0ms
(/ (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (* (sqrt (+ 1.0 (* z z))) x))
45.0ms
(sqrt (+ 1.0 (* z z)))
53.0ms
(sqrt (+ 1.0 (* z z)))

simplify127.0ms

Algorithm
egg-herbie
Counts
360 → 360
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
011704608
147804180
250024171

prune961.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.1b

regimes283.0ms

Accuracy

0% (0.9b remaining)

Error of 6.0b against oracle of 5.1b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02017
12017

end0.0ms

sample404.0ms

Algorithm
intervals
Results
235.0ms8599×body80valid