Details

Time bar (total: 4.9s)

sample31.0ms

Algorithm
intervals
Results
20.0ms271×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: 25.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(+ (* a c) (* b d))
24.7b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
3.0ms
(+ (* c c) (* d d))
5.0ms
(+ (* a c) (* b d))
11.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series139.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
34.0ms
(+ (* a c) (* b d))
78.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify138.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune204.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 16.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(fma a c (* b d))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
16.4b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
170×add-exp-log
92×prod-exp
63×div-exp
50×add-cbrt-cube
41×1-exp
17×cbrt-unprod
16×cbrt-undiv
15×rec-exp
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity times-frac
9×pow1
7×associate-*r* associate-*l*
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×pow-flip frac-2neg pow-prod-down clear-num associate-/r*
1×frac-times associate-*r/ associate-*l/ *-commutative fma-udef inv-pow unswap-sqr
Counts
4 → 145
Calls
4 calls:
5.0ms
(/ 1 (* (hypot c d) 1))
0.0ms
(fma a c (* b d))
25.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
3.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series387.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 1 (* (hypot c d) 1))
37.0ms
(fma a c (* b d))
182.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
112.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify47.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04861191
11654892
25002884

prune278.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.3b
(fma a c (* b d))
16.4b
(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

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:
0.0ms
(hypot c d)
7.0ms
(/ (/ (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))

series310.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(hypot c d)
120.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
36.0ms
(fma a c (* b d))
110.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify78.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune294.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (* (hypot c d) 1))
0.3b
(fma a c (* b d))
7.6b
(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
8.8b
(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
892×times-frac
402×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
384×sqrt-prod
161×associate-/l*
41×add-exp-log
32×add-cbrt-cube
24×div-inv
22×div-exp
16×cbrt-undiv
13×associate-/r*
6×prod-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg 1-exp clear-num cbrt-unprod
2×associate-/l/
1×fma-udef
Counts
4 → 529
Calls
4 calls:
39.0ms
(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (* (hypot c d) 1))
0.0ms
(fma a c (* b d))
11.0ms
(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
3.0ms
(/ (fma a c (* b d)) (sqrt (hypot c d)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(/ (/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (* (hypot c d) 1))
36.0ms
(fma a c (* b d))
110.0ms
(/ (/ (fma a c (* b d)) (sqrt (hypot c d))) (sqrt (hypot c d)))
194.0ms
(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify98.0ms

Algorithm
egg-herbie
Counts
541 → 541
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012378471
150017489

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.9b

regimes205.0ms

Accuracy

38.2% (7.2b remaining)

Error of 12.7b against oracle of 5.4b and baseline of 17.1b

bsearch85.0ms

Steps
ItersRangePoint
7
2.375231237295133e+141
4.635307654901863e+142
3.932038779064202e+142
9
-7.281669141149857e+115
-9.334314880381754e+110
-6.215723612105562e+115

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample863.0ms

Algorithm
intervals
Results
639.0ms8464×body80valid