Details

Time bar (total: 3.5s)

sample19.0ms

Algorithm
intervals
Results
9.0ms272×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.7b
(+ (* a c) (* b d))
28.6b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×flip3-+ associate-/r* flip-+ associate-/l*
2×pow1 expm1-log1p-u associate-/r/ log1p-expm1-u associate-/l/
1×cbrt-undiv +-commutative fma-def frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 47
Calls
2 calls:
2.0ms
(+ (* a c) (* b d))
11.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series112.0ms

Counts
2 → 6
Calls
2 calls:
32.0ms
(+ (* a c) (* b d))
80.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify88.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune160.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.5b
(fma a c (* b d))
18.6b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
154×add-exp-log
86×prod-exp
57×div-exp
44×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×rec-exp
11×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity times-frac
7×associate-*r* associate-*l*
5×pow1
3×expm1-log1p-u log1p-expm1-u div-inv associate-/l* add-log-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
3 → 112
Calls
3 calls:
21.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms
(fma a c (* b d))
3.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series327.0ms

Counts
3 → 9
Calls
3 calls:
177.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
36.0ms
(fma a c (* b d))
114.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify45.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04721079
11607796
25001794

prune216.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.5b
(fma a c (* b d))
18.6b
(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×fma-udef associate-/l/
Counts
3 → 89
Calls
3 calls:
6.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms
(fma a c (* b d))
2.0ms
(/ (fma a c (* b d)) (hypot c d))

series269.0ms

Counts
3 → 9
Calls
3 calls:
119.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
36.0ms
(fma a c (* b d))
112.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify79.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune268.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
0.5b
(fma a c (* b d))
18.7b
(/ (hypot c d) (fma a c (* b d)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
159×times-frac
120×div-exp
112×prod-exp
105×add-sqr-sqrt
93×*-un-lft-identity
91×add-cube-cbrt
64×1-exp
47×add-cbrt-cube
44×associate-*r*
43×rec-exp
19×cbrt-undiv
16×associate-/r*
12×pow1 cbrt-unprod
11×div-inv
7×associate-*l*
6×associate-/l*
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 270
Calls
4 calls:
5.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
35.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
0.0ms
(fma a c (* b d))
2.0ms
(/ (hypot c d) (fma a c (* b d)))

series427.0ms

Counts
4 → 12
Calls
4 calls:
113.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
184.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
37.0ms
(fma a c (* b d))
92.0ms
(/ (hypot c d) (fma a c (* b d)))

simplify90.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
010202692
139782350
250022153

prune491.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.8b

regimes185.0ms

Accuracy

34.6% (7.4b remaining)

Error of 13.3b against oracle of 5.9b and baseline of 17.2b

bsearch66.0ms

Steps
ItersRangePoint
9
1.8477608843692792e+99
4.399446247095774e+105
4.351899487575549e+105
5
-8.280096322353584e+183
-3.02511642897819e+183
-3.075733361844841e+183

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample504.0ms

Algorithm
intervals
Results
288.0ms8457×body80valid