Details

Time bar (total: 4.2s)

sample30.0ms

Algorithm
intervals
Results
19.0ms270×body80valid

simplify13.0ms

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: 28.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(- (* b c) (* a d))
27.5b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite19.0ms

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

series153.0ms

Counts
3 → 9
Calls
3 calls:
28.0ms
(+ (* c c) (* d d))
38.0ms
(- (* b c) (* a d))
86.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify39.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0314555
11341496
25001481

prune196.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.5b
(- (* b c) (* a d))
17.9b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite45.0ms

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:
5.0ms
(/ 1 (* (hypot c d) 1))
25.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series388.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(/ 1 (* (hypot c d) 1))
177.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
41.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify67.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05531207
123041003
25001995

prune335.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.5b
(- (* b c) (* a d))
17.9b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
10×add-exp-log add-cbrt-cube
6×associate-/r* div-inv
5×add-log-exp
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
3 → 121
Calls
3 calls:
10.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series278.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms
(- (* b c) (* a d))
118.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify52.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04491408
116571307
250011298

prune343.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (- (* b c) (* a d)))))
0.5b
(- (* b c) (* a d))
17.9b
(/ (hypot c d) (- (* b c) (* a d)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
171×times-frac
120×div-exp
112×prod-exp
109×add-sqr-sqrt
97×*-un-lft-identity
95×add-cube-cbrt
64×1-exp
50×associate-*r*
47×add-cbrt-cube
43×rec-exp
19×cbrt-undiv
18×associate-/r* associate-/r/
12×pow1 cbrt-unprod
11×div-inv
9×flip3-- flip--
7×associate-*l*
6×associate-/l* add-log-exp
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u
3×inv-pow
2×frac-2neg clear-num
1×frac-times sub-neg fma-neg diff-log associate-*r/ prod-diff associate-*l/ un-div-inv *-commutative
Counts
4 → 292
Calls
4 calls:
9.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
46.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (- (* b c) (* a d)))))
3.0ms
(- (* b c) (* a d))
5.0ms
(/ (hypot c d) (- (* b c) (* a d)))

series423.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
179.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (- (* b c) (* a d)))))
38.0ms
(- (* b c) (* a d))
90.0ms
(/ (hypot c d) (- (* b c) (* a d)))

simplify102.0ms

Algorithm
egg-herbie
Counts
304 → 304
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
011643296
146692898
250012690

prune534.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.7b

regimes206.0ms

Accuracy

36.2% (8.0b remaining)

Error of 12.7b against oracle of 4.7b and baseline of 17.2b

bsearch103.0ms

Steps
ItersRangePoint
6
1.2938133644756141e+156
1.1937552692612344e+157
1.6620599063431798e+156
5
-7.444366106241367e-58
-3.256405125857534e-58
-4.454705074921428e-58
10
-1.4188461903293662e+155
-2.402785143651615e+145
-1.8129434842371625e+150

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04324
15024
25324
35324

end0.0ms

sample741.0ms

Algorithm
intervals
Results
521.0ms8488×body80valid