Details

Time bar (total: 4.9s)

sample16.0ms

Algorithm
intervals
Results
7.0ms274×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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize7.0ms

Local error

Found 2 expressions with local error:

3.7b
(* y (+ 1.0 (* z z)))
5.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite18.0ms

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:
7.0ms
(* y (+ 1.0 (* z z)))
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series112.0ms

Counts
2 → 6
Calls
2 calls:
52.0ms
(* y (+ 1.0 (* z z)))
59.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify52.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune189.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.1b

localize8.0ms

Local error

Found 2 expressions with local error:

2.4b
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
3.4b
(/ (/ 1 x) (+ 1.0 (* z z)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
114×add-sqr-sqrt
88×*-un-lft-identity
86×add-cube-cbrt
46×add-exp-log
45×associate-*r*
28×add-cbrt-cube
23×div-exp
13×associate-*l* associate-/l*
12×cbrt-undiv
10×prod-exp div-inv
8×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 → 168
Calls
2 calls:
34.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
8.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

series111.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
52.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

simplify88.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08881623
143251446
250021361

prune386.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
2.4b
(* (/ 1.0 y) (/ (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite328.0ms

Algorithm
rewrite-expression-head
Rules
1529×times-frac
810×add-sqr-sqrt
681×*-un-lft-identity
673×add-cube-cbrt
560×sqrt-prod
510×associate-*r*
63×add-exp-log
52×div-inv
41×add-cbrt-cube
34×div-exp
30×unswap-sqr
20×sqrt-div
19×cbrt-undiv
16×associate-/r/
13×associate-*l* associate-/l*
12×prod-exp
10×flip3-+ flip-+
8×pow1 cbrt-unprod
6×associate-/r*
4×add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 731
Calls
4 calls:
10.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
239.0ms
(* (/ 1.0 y) (/ (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series221.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (/ 1 x) (sqrt (+ 1.0 (* z z))))
61.0ms
(* (/ 1.0 y) (/ (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
42.0ms
(sqrt (+ 1.0 (* z z)))
54.0ms
(sqrt (+ 1.0 (* z z)))

simplify143.0ms

Algorithm
egg-herbie
Counts
743 → 743
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0339710089
150019260

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (/ 1.0 y) (/ (/ 1 x) (sqrt (+ 1.0 (* z z))))) (/ 1 (sqrt (+ 1.0 (* z z)))))
2.5b
(* (/ 1.0 y) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
14.7b
(sqrt (+ 1.0 (* z z)))
14.7b
(sqrt (+ 1.0 (* z z)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
238×add-exp-log
186×times-frac
148×add-sqr-sqrt
108×associate-*r*
107×div-exp
99×*-un-lft-identity
95×add-cube-cbrt
94×prod-exp
90×add-cbrt-cube
60×sqrt-prod
34×cbrt-undiv
32×cbrt-unprod
21×rec-exp 1-exp
14×associate-*l* unswap-sqr
13×pow1
9×div-inv
8×sqrt-div
6×frac-times associate-*l/
4×flip3-+ associate-*r/ pow-prod-down associate-/r/ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 *-commutative
1×un-div-inv
Counts
4 → 270
Calls
4 calls:
64.0ms
(* (* (/ 1.0 y) (/ (/ 1 x) (sqrt (+ 1.0 (* z z))))) (/ 1 (sqrt (+ 1.0 (* z z)))))
53.0ms
(* (/ 1.0 y) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series249.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (* (/ 1.0 y) (/ (/ 1 x) (sqrt (+ 1.0 (* z z))))) (/ 1 (sqrt (+ 1.0 (* z z)))))
91.0ms
(* (/ 1.0 y) (/ (/ 1 x) (sqrt (+ 1.0 (* z z)))))
43.0ms
(sqrt (+ 1.0 (* z z)))
51.0ms
(sqrt (+ 1.0 (* z z)))

simplify60.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
015123209
150012720

prune578.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

regimes216.0ms

Accuracy

0% (1.2b remaining)

Error of 6.0b against oracle of 4.7b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01912
11912

end0.0ms

sample418.0ms

Algorithm
intervals
Results
240.0ms8683×body80valid