Details

Time bar (total: 8.5s)

sample18.0ms

Algorithm
intervals
Results
7.0ms269×body80valid

simplify15.0ms

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: 6.8b

localize8.0ms

Local error

Found 2 expressions with local error:

3.6b
(* y (+ 1.0 (* z z)))
3.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

rewrite33.0ms

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:
15.0ms
(* y (+ 1.0 (* z z)))
16.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series105.0ms

Counts
2 → 6
Calls
2 calls:
50.0ms
(* y (+ 1.0 (* z z)))
55.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify48.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0409511
11963443
25001443

prune156.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 2 expressions with local error:

2.9b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (+ 1.0 (* z z))))
4.0b
(/ (/ (cbrt 1.0) x) (+ 1.0 (* z z)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
275×times-frac
167×add-sqr-sqrt
141×add-cube-cbrt *-un-lft-identity
72×associate-*r*
65×cbrt-prod
43×add-exp-log
33×add-cbrt-cube
22×associate-/l*
18×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
10×div-inv
8×unswap-sqr
7×associate-*l*
4×pow1 associate-/r/
3×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 → 225
Calls
2 calls:
69.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (+ 1.0 (* z z))))
17.0ms
(/ (/ (cbrt 1.0) x) (+ 1.0 (* z z)))

series229.0ms

Counts
2 → 6
Calls
2 calls:
120.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (cbrt 1.0) x) (+ 1.0 (* z z))))
109.0ms
(/ (/ (cbrt 1.0) x) (+ 1.0 (* z z)))

simplify56.0ms

Algorithm
egg-herbie
Counts
231 → 231
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011932982
150012780

prune670.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
1.3b
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite230.0ms

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:
19.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
166.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
130.0ms
(* (/ (/ (* (cbrt 1.0) (cbrt 1.0)) y) (sqrt (+ 1.0 (* z z)))) (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))))
45.0ms
(sqrt (+ 1.0 (* z z)))
40.0ms
(sqrt (+ 1.0 (* z z)))

simplify104.0ms

Algorithm
egg-herbie
Counts
476 → 476
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
019008012
150017626

prune1.3s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
2.9b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
15.7b
(sqrt (+ 1.0 (* z z)))
15.7b
(sqrt (+ 1.0 (* z z)))

rewrite486.0ms

Algorithm
rewrite-expression-head
Rules
2612×times-frac
1290×add-sqr-sqrt
1160×add-cube-cbrt *-un-lft-identity
911×sqrt-prod
834×associate-*r*
395×cbrt-prod
63×add-exp-log
52×div-inv
51×add-cbrt-cube
30×unswap-sqr
29×cbrt-undiv div-exp
22×associate-/l*
20×sqrt-div
16×prod-exp associate-/r/ cbrt-unprod
10×flip3-+ flip-+
8×pow1
7×associate-*l*
6×associate-/r*
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 → 1114
Calls
4 calls:
19.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
335.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series317.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z))))
131.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) y) (/ (/ (/ (cbrt 1.0) x) (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
40.0ms
(sqrt (+ 1.0 (* z z)))
50.0ms
(sqrt (+ 1.0 (* z z)))

simplify187.0ms

Algorithm
egg-herbie
Counts
1126 → 1126
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500120224

prune3.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 5.2b

regimes289.0ms

Accuracy

0% (1.2b remaining)

Error of 6.1b against oracle of 4.8b and baseline of 6.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01615
11615

end0.0ms

sample465.0ms

Algorithm
intervals
Results
225.0ms8638×body80valid