Details

Time bar (total: 5.6s)

sample22.0ms

Algorithm
intervals
Results
13.0ms273×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: 6.3b

localize7.0ms

Local error

Found 2 expressions with local error:

4.5b
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
5.4b
(* y (+ 1.0 (* z z)))

rewrite19.0ms

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:
7.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
7.0ms
(* y (+ 1.0 (* z z)))

series109.0ms

Counts
2 → 6
Calls
2 calls:
57.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))
51.0ms
(* y (+ 1.0 (* z z)))

simplify48.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0416531
12028428
25001420

prune188.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
7.1b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite39.0ms

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:
5.0ms
(/ (/ 1.0 y) x)
17.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series77.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(/ (/ 1.0 y) x)
59.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify105.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
011383012
145962854
250022850

prune802.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt y)
0.5b
(cbrt y)
2.1b
(* (/ (fma z z 1.0) 1.0) (* (cbrt x) (cbrt y)))
4.3b
(/ (/ (/ 1 (* (cbrt y) (cbrt y))) (* (cbrt x) (cbrt x))) (* (/ (fma z z 1.0) 1.0) (* (cbrt x) (cbrt y))))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
441×add-exp-log
217×div-exp
161×prod-exp
135×add-cbrt-cube
101×cbrt-undiv
73×cbrt-unprod
40×times-frac
20×rec-exp 1-exp
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×associate-*l*
11×associate-/l*
9×pow1
6×cbrt-prod div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-prod-down
2×pow1/3 associate-*l/
1×frac-2neg associate-*r* clear-num associate-/r* associate-/r/ *-commutative associate-/l/
Counts
4 → 208
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
27.0ms
(* (/ (fma z z 1.0) 1.0) (* (cbrt x) (cbrt y)))
46.0ms
(/ (/ (/ 1 (* (cbrt y) (cbrt y))) (* (cbrt x) (cbrt x))) (* (/ (fma z z 1.0) 1.0) (* (cbrt x) (cbrt y))))

series602.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt y)
168.0ms
(cbrt y)
168.0ms
(* (/ (fma z z 1.0) 1.0) (* (cbrt x) (cbrt y)))
85.0ms
(/ (/ (/ 1 (* (cbrt y) (cbrt y))) (* (cbrt x) (cbrt x))) (* (/ (fma z z 1.0) 1.0) (* (cbrt x) (cbrt y))))

simplify50.0ms

Algorithm
egg-herbie
Counts
220 → 220
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
012133487
150012459

prune415.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
2.7b
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
18.8b
(sqrt (+ 1.0 (* z z)))
18.8b
(sqrt (+ 1.0 (* z z)))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
1464×times-frac
773×add-sqr-sqrt
655×*-un-lft-identity
649×add-cube-cbrt
297×sqrt-prod
264×associate-*r*
69×add-exp-log
55×div-inv
45×add-cbrt-cube
43×associate-/l*
39×div-exp
27×unswap-sqr
24×associate-*l*
22×cbrt-undiv
12×prod-exp
10×sqrt-div
8×pow1 cbrt-unprod
6×associate-/r* associate-/r/
5×flip3-+ flip-+
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l/
Counts
4 → 715
Calls
4 calls:
157.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
20.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series226.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
72.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
42.0ms
(sqrt (+ 1.0 (* z z)))
52.0ms
(sqrt (+ 1.0 (* z z)))

simplify139.0ms

Algorithm
egg-herbie
Counts
727 → 727
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
0275310743
1500210192

prune1.6s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.1b

regimes160.0ms

Accuracy

0% (1.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02015
12015

end0.0ms

sample606.0ms

Algorithm
intervals
Results
417.0ms8625×body80valid