Details

Time bar (total: 8.8s)

sample17.0ms

Algorithm
intervals
Results
7.0ms278×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.1b

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×expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u 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 → 74
Calls
2 calls:
15.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
14.0ms
(* y (+ 1.0 (* z z)))

series101.0ms

Counts
2 → 6
Calls
2 calls:
54.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
46.0ms
(* y (+ 1.0 (* z z)))

simplify47.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0416531
12028428
25001420

prune175.0ms

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)))

rewrite54.0ms

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 expm1-log1p-u frac-2neg clear-num associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
1×flip3-+ flip-+
Counts
2 → 268
Calls
2 calls:
10.0ms
(/ (/ 1.0 y) x)
28.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series71.0ms

Counts
2 → 6
Calls
2 calls:
17.0ms
(/ (/ 1.0 y) x)
55.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify106.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
011383012
145962854
250022850

prune729.0ms

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)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
410×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×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ div-exp flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
1×cbrt-div frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 449
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 y))
30.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
8.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series438.0ms

Counts
4 → 12
Calls
4 calls:
191.0ms
(cbrt (/ 1.0 y))
163.0ms
(/ (/ (cbrt (/ 1.0 y)) x) (sqrt (+ 1.0 (* z z))))
45.0ms
(sqrt (+ 1.0 (* z z)))
39.0ms
(sqrt (+ 1.0 (* z z)))

simplify139.0ms

Algorithm
egg-herbie
Counts
461 → 461
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
015427195
148296982
250016980

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.9b

localize17.0ms

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)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
2349×times-frac
1079×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×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-+ flip-+
2×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ hypot-def
1×cbrt-div frac-2neg pow1/3 clear-num associate-/l/
Counts
4 → 955
Calls
4 calls:
2.0ms
(cbrt (/ 1.0 y))
60.0ms
(/ (/ (/ (cbrt 1.0) (cbrt y)) x) (sqrt (+ 1.0 (* z z))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series476.0ms

Counts
4 → 12
Calls
4 calls:
194.0ms
(cbrt (/ 1.0 y))
195.0ms
(/ (/ (/ (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)))

simplify197.0ms

Algorithm
egg-herbie
Counts
967 → 967
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0303018527
1500118169

prune3.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.9b

regimes195.0ms

Accuracy

55.6% (0.5b remaining)

Error of 5.3b against oracle of 4.8b and baseline of 5.9b

bsearch52.0ms

Steps
ItersRangePoint
6
8.90194619562527e+91
1.0766047810163078e+93
3.3502160983592637e+92
8
-8.19698277052365e+162
-6.9631627878994466e+159
-7.594073760641085e+159

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0239
1239

end0.0ms

sample450.0ms

Algorithm
intervals
Results
226.0ms8567×body80valid