Details

Time bar (total: 10.8s)

sample32.0ms

Algorithm
intervals
Results
21.0ms274×body80valid

simplify20.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0215
1375
2615
3915
41155
51215
61215

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 2 expressions with local error:

3.6b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.3b
(* y (+ 1.0 (* z z)))

rewrite21.0ms

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:
8.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
11.0ms
(* y (+ 1.0 (* z z)))

series106.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
52.0ms
(* y (+ 1.0 (* z z)))

simplify48.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0409511
11963443
25001443

prune160.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
5.7b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite42.0ms

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 frac-2neg clear-num associate-/r/ associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 264
Calls
2 calls:
6.0ms
(/ (/ 1.0 y) x)
18.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series76.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 y) x)
58.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify108.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
011322994
145722919
250022919

prune699.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
3.4b
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
13.8b
(sqrt (+ 1.0 (* z z)))
13.8b
(sqrt (+ 1.0 (* z z)))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
3216×times-frac
1886×add-sqr-sqrt
1326×add-cube-cbrt *-un-lft-identity
682×cbrt-prod
617×sqrt-prod
426×associate-*r*
245×associate-*l*
99×unswap-sqr
70×associate-/l*
67×add-exp-log
61×div-inv
51×add-cbrt-cube
36×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
8×pow1 sqrt-div
6×associate-/r*
5×associate-/r/
4×flip3-+ flip-+ 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 → 1351
Calls
4 calls:
1.3s
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
60.0ms
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z)))))
115.0ms
(/ (/ (/ (cbrt 1.0) y) x) (sqrt (+ 1.0 (* z z))))
44.0ms
(sqrt (+ 1.0 (* z z)))
42.0ms
(sqrt (+ 1.0 (* z z)))

simplify277.0ms

Algorithm
egg-herbie
Counts
1363 → 1363
Iterations

Useful iterations: 1 (73.0ms)

IterNodesCost
0478426330
1500225983

prune4.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (cbrt 1.0) y) (* (sqrt (+ 1.0 (* z z))) x)))
2.2b
(/ (/ (cbrt 1.0) y) (* (sqrt (+ 1.0 (* z z))) x))
13.8b
(sqrt (+ 1.0 (* z z)))
13.8b
(sqrt (+ 1.0 (* z z)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
572×times-frac
319×add-sqr-sqrt
277×add-cube-cbrt *-un-lft-identity
264×cbrt-prod
245×associate-*l*
118×sqrt-prod
85×add-exp-log
62×add-cbrt-cube
39×cbrt-undiv div-exp
28×associate-*r*
23×prod-exp cbrt-unprod
22×associate-/l*
12×div-inv
11×unswap-sqr
8×pow1 sqrt-div
5×associate-*l/ associate-/r/
4×flip3-+ flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down clear-num associate-/r* *-commutative associate-/l/
Counts
4 → 422
Calls
4 calls:
176.0ms
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (cbrt 1.0) y) (* (sqrt (+ 1.0 (* z z))) x)))
15.0ms
(/ (/ (cbrt 1.0) y) (* (sqrt (+ 1.0 (* z z))) x))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series325.0ms

Counts
4 → 12
Calls
4 calls:
124.0ms
(* (/ (cbrt 1.0) (/ (sqrt (+ 1.0 (* z z))) (cbrt 1.0))) (/ (/ (cbrt 1.0) y) (* (sqrt (+ 1.0 (* z z))) x)))
113.0ms
(/ (/ (cbrt 1.0) y) (* (sqrt (+ 1.0 (* z z))) x))
39.0ms
(sqrt (+ 1.0 (* z z)))
48.0ms
(sqrt (+ 1.0 (* z z)))

simplify86.0ms

Algorithm
egg-herbie
Counts
434 → 434
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
015076852
150026513

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.1b

regimes175.0ms

Accuracy

0% (1.3b remaining)

Error of 6.3b against oracle of 5.0b and baseline of 6.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01715
11715

end0.0ms

sample715.0ms

Algorithm
intervals
Results
529.0ms8631×body80valid