Details

Time bar (total: 28.8s)

sample18.0ms

Algorithm
intervals
Results
7.0ms275×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: 4.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* z z))
2.9b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
3.8b
(* y (+ 1.0 (* z z)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
21×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
17×add-exp-log add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
5×pow1 add-log-exp
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* prod-exp cbrt-unprod flip-+ div-inv
2×associate-/r/
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num associate-/r* sum-log *-commutative associate-/l/ unswap-sqr
Counts
3 → 81
Calls
3 calls:
8.0ms
(+ 1.0 (* z z))
17.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
16.0ms
(* y (+ 1.0 (* z z)))

series131.0ms

Counts
3 → 9
Calls
3 calls:
29.0ms
(+ 1.0 (* z z))
56.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
47.0ms
(* y (+ 1.0 (* z z)))

simplify49.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 1 (11.0ms)

IterNodesCost
0432567
12077494
25002494

prune195.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (* z z))
2.9b
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))
2.9b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
299×times-frac
200×add-sqr-sqrt
153×add-cube-cbrt *-un-lft-identity
79×sqrt-prod
72×associate-*r*
29×add-exp-log add-cbrt-cube
22×associate-*l* associate-/l*
12×cbrt-undiv div-exp unswap-sqr
10×div-inv
6×prod-exp cbrt-unprod
5×pow1 add-log-exp
4×associate-/r/
3×flip3-+ associate-/r* flip-+
1×+-commutative frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num sum-log *-commutative associate-/l/
Counts
3 → 249
Calls
3 calls:
6.0ms
(+ 1.0 (* z z))
21.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))
76.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))

series296.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ 1.0 (* z z))
114.0ms
(/ (/ (sqrt 1.0) x) (+ 1.0 (* z z)))
154.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt 1.0) x) (+ 1.0 (* z z))))

simplify56.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
011352871
150012656

prune620.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (* z z))
0.3b
(/ (/ (sqrt (sqrt 1.0)) 1) (/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x)))
2.9b
(* (/ (sqrt 1.0) y) (/ (/ (sqrt (sqrt 1.0)) 1) (/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x))))
3.0b
(/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x))

rewrite2.8s

Algorithm
rewrite-expression-head
Rules
22990×times-frac
10728×sqrt-prod
10061×add-sqr-sqrt
9521×*-un-lft-identity
9476×add-cube-cbrt
3043×associate-*r*
457×div-inv
131×add-exp-log
129×associate-/r*
108×unswap-sqr
95×add-cbrt-cube
85×div-exp
66×associate-/r/
55×cbrt-undiv
34×associate-/l*
22×associate-*l*
20×prod-exp
14×cbrt-unprod
9×1-exp
6×pow1 add-log-exp
3×associate-/l/
2×frac-2neg flip3-+ clear-num flip-+
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 6568
Calls
4 calls:
6.0ms
(+ 1.0 (* z z))
109.0ms
(/ (/ (sqrt (sqrt 1.0)) 1) (/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x)))
1.4s
(* (/ (sqrt 1.0) y) (/ (/ (sqrt (sqrt 1.0)) 1) (/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x))))
30.0ms
(/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x))

series496.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(+ 1.0 (* z z))
99.0ms
(/ (/ (sqrt (sqrt 1.0)) 1) (/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x)))
185.0ms
(* (/ (sqrt 1.0) y) (/ (/ (sqrt (sqrt 1.0)) 1) (/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x))))
183.0ms
(/ (+ 1.0 (* z z)) (/ (sqrt (sqrt 1.0)) x))

simplify1.3s

Algorithm
egg-herbie
Counts
6580 → 6580
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
05612154351

prune21.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
2.9b
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
15.0b
(sqrt (+ 1.0 (* z z)))
15.0b
(sqrt (+ 1.0 (* z z)))

rewrite109.0ms

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:
43.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
48.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
5.0ms
(sqrt (+ 1.0 (* z z)))
5.0ms
(sqrt (+ 1.0 (* z z)))

series191.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z))))
59.0ms
(/ (/ 1.0 x) (* (* y (sqrt (+ 1.0 (* z z)))) (sqrt (+ 1.0 (* z z)))))
38.0ms
(sqrt (+ 1.0 (* z z)))
40.0ms
(sqrt (+ 1.0 (* z z)))

simplify71.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06101242
128861023
250011005

prune322.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.1b

regimes226.0ms

Accuracy

0% (1.6b remaining)

Error of 6.4b against oracle of 4.7b and baseline of 6.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0138
1138

end0.0ms

sample474.0ms

Algorithm
intervals
Results
232.0ms8597×body80valid