Details

Time bar (total: 4.5s)

sample16.0ms

Algorithm
intervals
Results
8.0ms273×body80valid

simplify14.0ms

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: 7.1b

localize13.0ms

Local error

Found 2 expressions with local error:

3.3b
(* 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×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)))
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series108.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(* y (+ 1.0 (* z z)))
54.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify50.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune156.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize9.0ms

Local error

Found 2 expressions with local error:

2.3b
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
5.2b
(/ (/ 1 x) (+ 1.0 (* z z)))

rewrite50.0ms

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:
31.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
11.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

series108.0ms

Counts
2 → 6
Calls
2 calls:
53.0ms
(* (/ 1.0 y) (/ (/ 1 x) (+ 1.0 (* z z))))
55.0ms
(/ (/ 1 x) (+ 1.0 (* z z)))

simplify94.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
08881623
143251446
250021361

prune328.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
1.1b
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z)))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
637×times-frac
481×add-sqr-sqrt
285×*-un-lft-identity
275×add-cube-cbrt
191×sqrt-prod
138×associate-*r*
84×associate-*l*
74×cbrt-prod
45×add-exp-log unswap-sqr
42×add-cbrt-cube
22×div-inv
21×cbrt-undiv div-exp
13×associate-/l*
10×sqrt-div
9×prod-exp cbrt-unprod
8×pow1
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×add-log-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 → 441
Calls
4 calls:
9.0ms
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
191.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z)))))
2.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series227.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (/ 1.0 y) (sqrt (+ 1.0 (* z z))))
62.0ms
(* (/ (/ 1.0 y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z)))))
47.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify107.0ms

Algorithm
egg-herbie
Counts
453 → 453
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
020266770
150016450

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.9b
(* (/ (/ 1 (* (cbrt y) (cbrt y))) 1) (* (/ (/ 1.0 (cbrt y)) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z))))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
879×add-exp-log
490×div-exp
345×prod-exp
208×add-cbrt-cube
122×cbrt-undiv
110×1-exp
86×cbrt-unprod
40×rec-exp
30×times-frac
25×associate-*l*
23×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
11×pow1
6×sqrt-prod
5×frac-times associate-*r/
4×sqrt-div div-inv add-log-exp
3×cbrt-prod pow-prod-down associate-*l/
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow1/3 associate-*r* *-commutative
Counts
4 → 274
Calls
4 calls:
1.0ms
(cbrt y)
111.0ms
(* (/ (/ 1 (* (cbrt y) (cbrt y))) 1) (* (/ (/ 1.0 (cbrt y)) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z))))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series357.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt y)
90.0ms
(* (/ (/ 1 (* (cbrt y) (cbrt y))) 1) (* (/ (/ 1.0 (cbrt y)) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1) x) (sqrt (+ 1.0 (* z z))))))
49.0ms
(sqrt (+ 1.0 (* z z)))
41.0ms
(sqrt (+ 1.0 (* z z)))

simplify81.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
016405847
150024633

prune517.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 5.5b

regimes183.0ms

Accuracy

0% (1.2b remaining)

Error of 6.0b against oracle of 4.8b and baseline of 6.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01812
11812

end0.0ms

sample427.0ms

Algorithm
intervals
Results
248.0ms8598×body80valid