Details

Time bar (total: 9.0s)

sample20.0ms

Algorithm
intervals
Results
9.0ms278×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: 6.7b

localize7.0ms

Local error

Found 2 expressions with local error:

4.2b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
4.5b
(* y (+ 1.0 (* z z)))

rewrite35.0ms

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:
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
16.0ms
(* y (+ 1.0 (* z z)))

series143.0ms

Counts
2 → 6
Calls
2 calls:
73.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
70.0ms
(* y (+ 1.0 (* z z)))

simplify47.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0409511
11963443
25001443

prune156.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.9b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
6.4b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite60.0ms

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:
11.0ms
(/ (/ 1.0 y) x)
28.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series69.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(/ (/ 1.0 y) x)
52.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify116.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011322994
145722919
250022919

prune698.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.9b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 y))
1.1b
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
408×add-sqr-sqrt
406×add-cube-cbrt *-un-lft-identity
286×cbrt-prod
165×sqrt-prod
52×associate-/l*
30×div-inv
9×add-exp-log
8×add-cbrt-cube
6×pow1 sqrt-div associate-/r*
4×add-log-exp
3×cbrt-undiv flip3-+ div-exp flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-div frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 439
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 y))
36.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series448.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(cbrt (/ 1.0 y))
164.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
45.0ms
(sqrt (+ 1.0 (* z z)))
38.0ms
(sqrt (+ 1.0 (* z z)))

simplify141.0ms

Algorithm
egg-herbie
Counts
451 → 451
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
015297159
147866956
250026916

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 y))
1.1b
(/ (/ (/ (cbrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
15.4b
(sqrt (+ 1.0 (* z z)))
15.4b
(sqrt (+ 1.0 (* z z)))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
2349×times-frac
1077×add-sqr-sqrt
1075×add-cube-cbrt *-un-lft-identity
769×cbrt-prod
381×sqrt-prod
124×associate-/l*
30×div-inv
13×add-exp-log
11×add-cbrt-cube
6×pow1 cbrt-undiv sqrt-div div-exp associate-/r*
4×add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/
1×cbrt-div frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 945
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 y))
66.0ms
(/ (/ (/ (cbrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
6.0ms
(sqrt (+ 1.0 (* z z)))

series684.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(cbrt (/ 1.0 y))
404.0ms
(/ (/ (/ (cbrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
47.0ms
(sqrt (+ 1.0 (* z z)))
40.0ms
(sqrt (+ 1.0 (* z z)))

simplify196.0ms

Algorithm
egg-herbie
Counts
957 → 957
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0301718489
1500218139

prune3.7s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.9b

regimes216.0ms

Accuracy

79.3% (0.2b remaining)

Error of 5.0b against oracle of 4.8b and baseline of 5.9b

bsearch67.0ms

Steps
ItersRangePoint
8
9.207344403156347e+67
1.2323468673482036e+72
1.7144269134100035e+68
9
-1866581624808.8018
-3035742.345269493
-38289380947.14346

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02923
12923

end0.0ms

sample473.0ms

Algorithm
intervals
Results
228.0ms8567×body80valid