Details

Time bar (total: 3.9s)

sample19.0ms

Algorithm
intervals
Results
9.0ms271×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize12.0ms

Local error

Found 2 expressions with local error:

0.5b
(+ (* a c) (* b d))
25.5b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite13.0ms

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:
4.0ms
(+ (* a c) (* b d))
8.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series113.0ms

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

simplify87.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
0244458
1872411
23164403
35001403

prune155.0ms

Filtered
53 candidates to 44 candidates (83.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.5b
(fma a c (* b d))
16.8b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
86×prod-exp
57×div-exp
45×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×add-sqr-sqrt rec-exp
10×add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r* associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv associate-/l*
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
4 → 122
Calls
4 calls:
1.0ms
(hypot c d)
12.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
1.0ms
(fma a c (* b d))
4.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series375.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
179.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
36.0ms
(fma a c (* b d))
113.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify45.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861106
11625820
25001818

prune262.0ms

Filtered
134 candidates to 72 candidates (53.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.5b
(fma a c (* b d))
16.8b
(/ (fma a c (* b d)) (hypot c d))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×hypot-udef fma-udef associate-/l/
Counts
4 → 99
Calls
4 calls:
1.0ms
(hypot c d)
7.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
1.0ms
(fma a c (* b d))
3.0ms
(/ (fma a c (* b d)) (hypot c d))

series307.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
112.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
39.0ms
(fma a c (* b d))
109.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify77.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune298.0ms

Filtered
111 candidates to 89 candidates (80.2%)
Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.5b

localize16.0ms

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))
16.8b
(/ (hypot c d) (fma a c (* b d)))

rewrite44.0ms

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:
6.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
21.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
1.0ms
(fma a c (* b d))
3.0ms
(/ (hypot c d) (fma a c (* b d)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
178.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
40.0ms
(fma a c (* b d))
89.0ms
(/ (hypot c d) (fma a c (* b d)))

simplify85.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
010202692
139782350
250022153

prune505.0ms

Filtered
282 candidates to 139 candidates (49.3%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.5b

regimes196.0ms

Accuracy

41% (6.9b remaining)

Error of 12.4b against oracle of 5.5b and baseline of 17.1b

bsearch71.0ms

Steps
ItersRangePoint
9
9.440790057172212e+149
1.0059809584366412e+156
7.212493497445931e+153
6
-4.494070164601314e+110
-1.0328813798619898e+110
-3.6474152257737815e+110

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03116
13616
23616

end0.0ms

sample711.0ms

Algorithm
intervals
Results
503.0ms8470×body80valid