Details

Time bar (total: 5.4s)

sample27.0ms

Algorithm
intervals
Results
17.0ms266×body80valid

simplify23.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0215
1404
2694
31044
41464
51604
61604

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.6b

localize11.0ms

Local error

Found 2 expressions with local error:

3.1b
(* y (+ 1.0 (* z z)))
3.3b
(/ (/ 1.0 x) (* 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
(* y (+ 1.0 (* z z)))
9.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

series129.0ms

Counts
2 → 6
Calls
2 calls:
63.0ms
(* y (+ 1.0 (* z z)))
66.0ms
(/ (/ 1.0 x) (* y (+ 1.0 (* z z))))

simplify63.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0416531
12028428
25001420

prune232.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b
(/ (/ 1.0 y) x)
4.6b
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

rewrite48.0ms

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:
6.0ms
(/ (/ 1.0 y) x)
18.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

series83.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(/ (/ 1.0 y) x)
62.0ms
(/ (/ (/ 1.0 y) x) (+ 1.0 (* z z)))

simplify133.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
011383012
145962854
250022850

prune859.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
2.2b
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
13.0b
(sqrt (+ 1.0 (* z z)))
13.0b
(sqrt (+ 1.0 (* z z)))

rewrite270.0ms

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:
173.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
23.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
3.0ms
(sqrt (+ 1.0 (* z z)))
3.0ms
(sqrt (+ 1.0 (* z z)))

series251.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (/ 1.0 (sqrt (+ 1.0 (* z z)))) (/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z)))))
82.0ms
(/ (/ (/ 1 y) x) (sqrt (+ 1.0 (* z z))))
45.0ms
(sqrt (+ 1.0 (* z z)))
56.0ms
(sqrt (+ 1.0 (* z z)))

simplify158.0ms

Algorithm
egg-herbie
Counts
727 → 727
Iterations

Useful iterations: 1 (60.0ms)

IterNodesCost
0276310745
1500210192

prune1.7s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.4b
(/ 1.0 (* x y))
4.6b
(/ (/ 1.0 (* x y)) (+ 1.0 (* z z)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
20×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log add-cbrt-cube
10×associate-/l*
7×cbrt-undiv div-exp
6×div-inv
4×associate-/r*
2×pow1 expm1-log1p-u frac-2neg prod-exp clear-num associate-/r/ cbrt-unprod log1p-expm1-u add-log-exp
1×flip3-+ flip-+ associate-/l/
Counts
2 → 75
Calls
2 calls:
3.0ms
(/ 1.0 (* x y))
8.0ms
(/ (/ 1.0 (* x y)) (+ 1.0 (* z z)))

series86.0ms

Counts
2 → 6
Calls
2 calls:
23.0ms
(/ 1.0 (* x y))
64.0ms
(/ (/ 1.0 (* x y)) (+ 1.0 (* z z)))

simplify61.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0361588
11639520
25001516

prune196.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 3.4b

regimes150.0ms

Accuracy

83.1% (0.3b remaining)

Error of 5.1b against oracle of 4.9b and baseline of 6.4b

bsearch113.0ms

Steps
ItersRangePoint
9
1462220638078.2073
1.3445511102506227e+18
643945125486439.2
9
-1.033873228062193e+38
-5.744531494618664e+32
-5.7998173554975605e+32

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
12915

end0.0ms

sample757.0ms

Algorithm
intervals
Results
570.0ms8589×body80valid