Details

Time bar (total: 3.6s)

sample20.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
4.0ms256×pre80true

simplify69.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0236
1526
21176
32406
44786
59476
618446
750016

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 22.2b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
21.4b
(/ (fma x x (* y y)) (+ x y))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
160×*-un-lft-identity
116×add-sqr-sqrt
78×add-cube-cbrt
22×associate-/r* distribute-lft-out
19×distribute-lft-out-- difference-of-squares
15×associate-/r/
9×add-exp-log add-cbrt-cube
8×div-inv associate-/l*
7×flip3-+ flip-+
4×cbrt-undiv div-exp
2×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
1×flip3-- div-sub flip--
Counts
2 → 168
Calls
2 calls:
15.0ms
(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
5.0ms
(/ (fma x x (* y y)) (+ x y))

series138.0ms

Counts
2 → 6
Calls
2 calls:
68.0ms
(/ (- x y) (/ (fma x x (* y y)) (+ x y)))
69.0ms
(/ (fma x x (* y y)) (+ x y))

simplify76.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
06402000
127371832
250011825

prune334.0ms

Filtered
174 candidates to 117 candidates (67.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot x y)
0.0b
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b
(* (hypot x y) (/ (hypot x y) (+ x y)))
0.0b
(/ (hypot x y) (+ x y))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×add-sqr-sqrt
30×times-frac
24×add-cube-cbrt
20×add-exp-log add-cbrt-cube
18×associate-*r*
8×associate-/l*
7×distribute-lft-out
6×pow1 cbrt-undiv div-exp
5×associate-/r* associate-/r/
4×expm1-log1p-u prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×associate-*l* div-inv
2×frac-2neg flip3-+ associate-*r/ clear-num flip-+ associate-/l/ distribute-lft-out-- difference-of-squares unswap-sqr
1×hypot-udef flip3-- div-sub pow-prod-down *-commutative flip--
Counts
4 → 117
Calls
4 calls:
0.0ms
(hypot x y)
12.0ms
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
15.0ms
(* (hypot x y) (/ (hypot x y) (+ x y)))
5.0ms
(/ (hypot x y) (+ x y))

series316.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot x y)
91.0ms
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
89.0ms
(* (hypot x y) (/ (hypot x y) (+ x y)))
90.0ms
(/ (hypot x y) (+ x y))

simplify49.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0378858
11715740
25001733

prune256.0ms

Filtered
129 candidates to 96 candidates (74.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
0.0b
(* (hypot x y) (/ (hypot x y) (+ x y)))
0.0b
(/ (hypot x y) (+ x y))
0.3b
(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×add-sqr-sqrt
30×times-frac
24×add-cube-cbrt
20×add-exp-log add-cbrt-cube
18×associate-*r*
8×associate-/l*
7×distribute-lft-out
6×pow1 cbrt-undiv div-exp
5×associate-/r* associate-/r/ log1p-expm1-u
4×expm1-log1p-u prod-exp cbrt-unprod add-log-exp
3×associate-*l* div-inv
2×frac-2neg flip3-+ associate-*r/ clear-num flip-+ associate-/l/ distribute-lft-out-- difference-of-squares unswap-sqr
1×expm1-log1p flip3-- div-sub pow-prod-down *-commutative flip-- expm1-udef
Counts
4 → 118
Calls
4 calls:
13.0ms
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
15.0ms
(* (hypot x y) (/ (hypot x y) (+ x y)))
5.0ms
(/ (hypot x y) (+ x y))
0.0ms
(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y))))
89.0ms
(* (hypot x y) (/ (hypot x y) (+ x y)))
95.0ms
(/ (hypot x y) (+ x y))
120.0ms
(expm1 (/ (- x y) (* (hypot x y) (/ (hypot x y) (+ x y)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0391948
11740816
25001809

prune310.0ms

Filtered
130 candidates to 93 candidates (71.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- x y) (* (hypot x y) (/ 1 (/ (+ x y) (hypot x y)))))
0.0b
(* (hypot x y) (/ 1 (/ (+ x y) (hypot x y))))
0.0b
(/ (+ x y) (hypot x y))
0.3b
(expm1 (/ (- x y) (* (hypot x y) (/ 1 (/ (+ x y) (hypot x y))))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
107×times-frac
89×*-un-lft-identity
75×add-sqr-sqrt
57×add-cube-cbrt
53×add-exp-log associate-*r*
29×add-cbrt-cube
23×div-exp
14×prod-exp
13×distribute-lft-out
11×cbrt-undiv
9×associate-/l*
6×pow1 cbrt-unprod div-inv
5×log1p-expm1-u unswap-sqr
4×expm1-log1p-u rec-exp 1-exp associate-/r* associate-/l/ add-log-exp
3×associate-*l* associate-/r/
2×frac-2neg associate-*r/ clear-num un-div-inv distribute-lft-out-- difference-of-squares
1×expm1-log1p flip3-- flip3-+ div-sub pow-prod-down *-commutative flip-- flip-+ expm1-udef
Counts
4 → 170
Calls
4 calls:
20.0ms
(/ (- x y) (* (hypot x y) (/ 1 (/ (+ x y) (hypot x y)))))
28.0ms
(* (hypot x y) (/ 1 (/ (+ x y) (hypot x y))))
8.0ms
(/ (+ x y) (hypot x y))
0.0ms
(expm1 (/ (- x y) (* (hypot x y) (/ 1 (/ (+ x y) (hypot x y))))))

series392.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (- x y) (* (hypot x y) (/ 1 (/ (+ x y) (hypot x y)))))
90.0ms
(* (hypot x y) (/ 1 (/ (+ x y) (hypot x y))))
90.0ms
(/ (+ x y) (hypot x y))
120.0ms
(expm1 (/ (- x y) (* (hypot x y) (/ 1 (/ (+ x y) (hypot x y))))))

simplify76.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06821494
134451269
250021187

prune430.0ms

Filtered
182 candidates to 123 candidates (67.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes35.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01610
11610

end0.0ms

sample471.0ms

Algorithm
intervals
Results
223.0ms8000×body80valid
111.0ms8000×pre80true