Details

Time bar (total: 4.1s)

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: 28.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.0b
(+ (* a c) (* b d))
27.6b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite18.0ms

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))
3.0ms
(+ (* a c) (* b d))
11.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series151.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* c c) (* d d))
37.0ms
(+ (* a c) (* b d))
85.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify138.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune222.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 18.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
17.6b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite39.0ms

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 hypot-udef associate-*r/ associate-*l/ *-commutative inv-pow unswap-sqr
Counts
4 → 145
Calls
4 calls:
0.0ms
(hypot c d)
4.0ms
(/ 1 (* (hypot c d) 1))
22.0ms
(* (/ 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))

series403.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
61.0ms
(/ 1 (* (hypot c d) 1))
182.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
113.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify46.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04931177
11635880
25001872

prune306.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.0b
(hypot c d)
0.1b
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
17.6b
(/ (fma a c (* b d)) (hypot c d))

rewrite13.0ms

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×hypot-udef frac-2neg 1-exp clear-num cbrt-unprod
1×associate-/l/
Counts
4 → 99
Calls
4 calls:
0.0ms
(hypot c d)
0.0ms
(hypot c d)
7.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
2.0ms
(/ (fma a c (* b d)) (hypot c d))

series333.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(hypot c d)
51.0ms
(hypot c d)
119.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
117.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify82.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (68.0ms)

IterNodesCost
0301780
11076689
23153689
35001681

prune331.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
0.2b
(/ 1 (/ (hypot c d) (fma a c (* b d))))
17.6b
(/ (hypot c d) (fma a c (* b d)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
260×times-frac
124×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
81×add-exp-log
50×div-exp associate-/l*
32×add-cbrt-cube
17×associate-/r*
16×cbrt-undiv
15×1-exp div-inv
14×prod-exp
8×rec-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num associate-/r/ cbrt-unprod
1×hypot-udef pow-flip associate-/l/ inv-pow
Counts
4 → 246
Calls
4 calls:
0.0ms
(hypot c d)
17.0ms
(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
5.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
2.0ms
(/ (hypot c d) (fma a c (* b d)))

series459.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(hypot c d)
192.0ms
(/ (/ 1 (/ (hypot c d) (fma a c (* b d)))) (* (hypot c d) 1))
119.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
95.0ms
(/ (hypot c d) (fma a c (* b d)))

simplify80.0ms

Algorithm
egg-herbie
Counts
258 → 258
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07992576
136562248
250012086

prune554.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.5b

regimes240.0ms

Accuracy

33.3% (7.5b remaining)

Error of 13.2b against oracle of 5.7b and baseline of 16.9b

bsearch63.0ms

Steps
ItersRangePoint
5
1.1874868645648804e+84
3.824179182553312e+84
3.559188999299462e+84
8
-1.6993806662071022e+156
-3.922170094862376e+153
-3.776971399950804e+155

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
13115
23115

end0.0ms

sample494.0ms

Algorithm
intervals
Results
289.0ms8456×body80valid