Details

Time bar (total: 5.3s)

sample27.0ms

Algorithm
intervals
Results
12.0ms408×body80valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0227
1557
21017
31827
43357
57317
618287
750017

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (* y y))
5.6b
(- (+ (* x x) (* y y)) (* z z))
28.5b
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-exp-log add-sqr-sqrt add-cbrt-cube
5×add-cube-cbrt *-un-lft-identity
4×times-frac associate-/l*
3×pow1 difference-of-squares
2×cbrt-undiv flip3-- diff-log div-exp sum-log flip-- associate-/l/
1×+-commutative sub-neg frac-2neg flip3-+ div-sub prod-exp associate--l+ clear-num associate-/r* cbrt-unprod flip-+ div-inv
Counts
3 → 52
Calls
3 calls:
8.0ms
(+ (* x x) (* y y))
39.0ms
(- (+ (* x x) (* y y)) (* z z))
73.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series134.0ms

Counts
3 → 9
Calls
3 calls:
24.0ms
(+ (* x x) (* y y))
39.0ms
(- (+ (* x x) (* y y)) (* z z))
71.0ms
(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0337520
11492454
25001446

prune148.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 13.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
0.2b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
10.0b
(/ (pow z 2) y)
10.6b
(/ (pow x 2) y)

rewrite376.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
52×times-frac
47×*-un-lft-identity
40×add-cube-cbrt
25×unpow-prod-down
16×add-exp-log associate-/l*
10×associate-*r* add-cbrt-cube
9×unpow2 sqr-pow
6×pow1 div-exp associate-/r* add-log-exp
5×difference-of-squares
4×associate-*r/
3×distribute-rgt-in distribute-lft-in associate-*l*
2×cbrt-undiv pow-to-exp sub-neg frac-2neg flip3-+ pow-exp associate--l+ clear-num frac-sub flip-+ div-inv distribute-lft-out distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 145
Calls
4 calls:
17.0ms
(+ y (/ (pow x 2) y))
333.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
11.0ms
(/ (pow z 2) y)
9.0ms
(/ (pow x 2) y)

series109.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ y (/ (pow x 2) y))
47.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
16.0ms
(/ (pow z 2) y)
19.0ms
(/ (pow x 2) y)

simplify54.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0494902
11944815
25003809

prune354.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x 2) y))
0.2b
(/ (pow z (/ 2 2)) (/ y z))
0.2b
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z (/ 2 2)) (/ y z))))
10.6b
(/ (pow x 2) y)

rewrite478.0ms

Algorithm
rewrite-expression-head
Rules
196×times-frac
130×add-sqr-sqrt
114×*-un-lft-identity
107×add-cube-cbrt
56×unpow-prod-down
24×add-exp-log
20×sqr-pow
16×associate-/r*
15×associate-/l*
13×add-cbrt-cube
12×div-exp associate-*r*
10×div-inv
7×difference-of-squares
6×pow1 add-log-exp
4×cbrt-undiv associate-*r/ unpow2
3×distribute-rgt-in pow-to-exp distribute-lft-in associate-*l* pow-exp
2×sub-neg frac-2neg flip3-+ associate--l+ clear-num frac-sub flip-+ distribute-lft-out distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log associate-/r/ *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 228
Calls
4 calls:
18.0ms
(+ y (/ (pow x 2) y))
14.0ms
(/ (pow z (/ 2 2)) (/ y z))
427.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z (/ 2 2)) (/ y z))))
9.0ms
(/ (pow x 2) y)

series108.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(+ y (/ (pow x 2) y))
21.0ms
(/ (pow z (/ 2 2)) (/ y z))
48.0ms
(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z (/ 2 2)) (/ y z))))
17.0ms
(/ (pow x 2) y)

simplify118.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 2 (98.0ms)

IterNodesCost
09081669
142491444
250011439

prune481.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ y (/ (pow x (/ 2 2)) (/ y x)))
0.2b
(/ (pow z (/ 2 2)) (/ y z))
0.2b
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z (/ 2 2)) (/ y z))))
0.2b
(/ (pow x (/ 2 2)) (/ y x))

rewrite902.0ms

Algorithm
rewrite-expression-head
Rules
335×times-frac
197×add-sqr-sqrt
181×*-un-lft-identity
174×add-cube-cbrt
86×unpow-prod-down
32×add-exp-log
30×sqr-pow
26×associate-/r*
18×div-exp div-inv
16×add-cbrt-cube
14×associate-/l*
12×associate-*r*
7×difference-of-squares
6×pow1 cbrt-undiv add-log-exp
4×pow-to-exp associate-*r/ pow-exp
3×distribute-rgt-in distribute-lft-in associate-*l*
2×sub-neg frac-2neg flip3-+ associate--l+ clear-num associate-/r/ frac-sub flip-+ distribute-lft-out distribute-lft-out--
1×+-commutative flip3-- pow-prod-down prod-exp sum-log *-commutative flip-- cbrt-unprod unswap-sqr
Counts
4 → 309
Calls
4 calls:
39.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
14.0ms
(/ (pow z (/ 2 2)) (/ y z))
816.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z (/ 2 2)) (/ y z))))
16.0ms
(/ (pow x (/ 2 2)) (/ y x))

series113.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(+ y (/ (pow x (/ 2 2)) (/ y x)))
17.0ms
(/ (pow z (/ 2 2)) (/ y z))
53.0ms
(* 0.5 (- (+ y (/ (pow x (/ 2 2)) (/ y x))) (/ (pow z (/ 2 2)) (/ y z))))
18.0ms
(/ (pow x (/ 2 2)) (/ y x))

simplify54.0ms

Algorithm
egg-herbie
Counts
321 → 321
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012702436
150022078

prune638.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

regimes118.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219
1239
2239

end0.0ms

sample832.0ms

Algorithm
intervals
Results
433.0ms13746×body80valid