Details

Time bar (total: 4.5s)

sample21.0ms

Algorithm
intervals
Results
8.0ms270×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
22.2b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite41.0ms

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
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
8.0ms
(+ (* c c) (* d d))
8.0ms
(- (* b c) (* a d))
24.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series168.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* c c) (* d d))
44.0ms
(- (* b c) (* a d))
95.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify38.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune191.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 11.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
13.5b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite90.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
10.0ms
(/ 1 (* (hypot c d) 1))
49.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
8.0ms
(- (* b c) (* a d))
17.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series407.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 1 (* (hypot c d) 1))
185.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
44.0ms
(- (* b c) (* a d))
125.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
05531207
123041003
25001995

prune321.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b
(- (* b c) (* a d))
13.5b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
0.0ms
(hypot c d)
18.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
8.0ms
(- (* b c) (* a d))
21.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series351.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(hypot c d)
126.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
43.0ms
(- (* b c) (* a d))
132.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify50.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04581435
116671331
250011322

prune355.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
0.2b
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
0.5b
(- (* b c) (* a d))
13.6b
(/ (hypot c d) (- (* b c) (* a d)))

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
528×times-frac
255×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
56×associate-/l*
39×associate-/r/
36×add-exp-log
23×div-inv
22×div-exp
21×associate-/r*
20×add-cbrt-cube
18×flip3-- flip--
10×cbrt-undiv
6×add-log-exp
5×pow1
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
3×frac-2neg clear-num
1×sub-neg pow-flip fma-neg diff-log prod-diff associate-/l/ inv-pow
Counts
4 → 359
Calls
4 calls:
40.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
19.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
8.0ms
(- (* b c) (* a d))
12.0ms
(/ (hypot c d) (- (* b c) (* a d)))

series461.0ms

Counts
4 → 12
Calls
4 calls:
192.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
123.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
46.0ms
(- (* b c) (* a d))
100.0ms
(/ (hypot c d) (- (* b c) (* a d)))

simplify71.0ms

Algorithm
egg-herbie
Counts
371 → 371
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012945404
150024894

prune809.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.8b

regimes145.0ms

Accuracy

30.9% (8.3b remaining)

Error of 12.8b against oracle of 4.5b and baseline of 16.5b

bsearch70.0ms

Steps
ItersRangePoint
10
2.714157836303516e+105
2.557420317019269e+120
1.353255254313691e+119
9
-1.6823650368807856e+194
-1.6152694645605263e+185
-3.380617245803456e+187

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02813
12913
22913

end0.0ms

sample589.0ms

Algorithm
intervals
Results
291.0ms8503×body80valid