Details

Time bar (total: 4.8s)

sample30.0ms

Algorithm
intervals
Results
20.0ms279×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.9b

localize7.0ms

Local error

Found 2 expressions with local error:

3.4b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.1b
(* y (+ 1.0 (* z z)))

rewrite20.0ms

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:
11.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms
(* y (+ 1.0 (* z z)))

series109.0ms

Counts
2 → 6
Calls
2 calls:
59.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
50.0ms
(* y (+ 1.0 (* z z)))

simplify47.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0409511
11963443
25001443

prune162.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
3.4b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
14.1b
(sqrt (+ 1.0 (* z z)))
14.1b
(sqrt (+ 1.0 (* z z)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
30×add-exp-log add-cbrt-cube
28×sqrt-div
24×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
16×associate-*r/
14×flip3-+ flip-+
13×associate-/l*
11×pow1
9×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
8×frac-times associate-/r/
6×associate-*r*
4×associate-*l/ add-log-exp
3×pow-prod-down div-inv
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-2neg associate-*l* clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 117
Calls
4 calls:
19.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
24.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (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:
51.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
61.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
47.0ms
(sqrt (+ 1.0 (* z z)))
43.0ms
(sqrt (+ 1.0 (* z z)))

simplify70.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06101242
128861023
250011005

prune321.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
1.9b
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
14.1b
(sqrt (+ 1.0 (* z z)))
14.1b
(sqrt (+ 1.0 (* z z)))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
650×times-frac
443×add-sqr-sqrt
293×add-cube-cbrt *-un-lft-identity
191×sqrt-prod
138×associate-*r*
127×cbrt-prod
63×add-exp-log
52×add-cbrt-cube
48×associate-*l*
35×unswap-sqr
30×cbrt-undiv div-exp
22×div-inv associate-/l*
15×prod-exp cbrt-unprod
10×sqrt-div
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 → 464
Calls
4 calls:
12.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
142.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series346.0ms

Counts
4 → 12
Calls
4 calls:
103.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
152.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
41.0ms
(sqrt (+ 1.0 (* z z)))
50.0ms
(sqrt (+ 1.0 (* z z)))

simplify107.0ms

Algorithm
egg-herbie
Counts
476 → 476
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
019008012
150017626

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize19.0ms

Local error

Found 4 expressions with local error:

14.1b
(sqrt (+ 1.0 (* z z)))
14.1b
(sqrt (+ 1.0 (* z z)))
14.1b
(sqrt (+ 1.0 (* z z)))
14.1b
(sqrt (+ 1.0 (* z z)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
8×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 60
Calls
4 calls:
3.0ms
(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)))

series175.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(sqrt (+ 1.0 (* z z)))
44.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))
47.0ms
(sqrt (+ 1.0 (* z z)))

simplify64.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (57.0ms)

IterNodesCost
0135420
1442408
21946400
35001396

prune285.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

regimes271.0ms

Accuracy

23.2% (0.8b remaining)

Error of 5.8b against oracle of 5.0b and baseline of 6.0b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03146
13146

end0.0ms

sample815.0ms

Algorithm
intervals
Results
627.0ms8663×body80valid