Details

Time bar (total: 5.5s)

sample35.0ms

Algorithm
intervals
Results
24.0ms268×body80valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(- (* b c) (* a d))
26.2b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite17.0ms

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))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series154.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
41.0ms
(- (* b c) (* a d))
87.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify42.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0314555
11341496
25001481

prune196.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 12.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(- (* b c) (* a d))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
15.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite41.0ms

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:
4.0ms
(/ 1 (* (hypot c d) 1))
3.0ms
(- (* b c) (* a d))
23.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series383.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (* (hypot c d) 1))
38.0ms
(- (* b c) (* a d))
175.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
116.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify63.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
05531207
123041003
25001995

prune319.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.2b
(- (* b c) (* a d))
15.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

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:
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series268.0ms

Counts
3 → 9
Calls
3 calls:
114.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
40.0ms
(- (* b c) (* a d))
113.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify51.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04491408
116571307
250011298

prune329.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (/ (- (* b c) (* a d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (hypot c d))
0.2b
(- (* b c) (* a d))
7.5b
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))
7.9b
(/ (/ (- (* b c) (* a d)) (sqrt (hypot c d))) (sqrt (hypot c d)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
1644×times-frac
785×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
624×sqrt-prod
161×associate-/l*
38×div-inv
20×add-exp-log add-cbrt-cube
15×associate-/r*
10×cbrt-undiv div-exp
6×div-sub add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/
3×frac-2neg clear-num
2×flip3-- flip--
1×sub-neg fma-neg diff-log prod-diff
Counts
4 → 805
Calls
4 calls:
44.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (hypot c d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))
14.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (hypot c d))) (sqrt (hypot c d)))

series474.0ms

Counts
4 → 12
Calls
4 calls:
119.0ms
(/ (/ (/ (- (* b c) (* a d)) (sqrt (hypot c d))) (sqrt (hypot c d))) (hypot c d))
43.0ms
(- (* b c) (* a d))
196.0ms
(/ (- (* b c) (* a d)) (sqrt (hypot c d)))
116.0ms
(/ (/ (- (* b c) (* a d)) (sqrt (hypot c d))) (sqrt (hypot c d)))

simplify173.0ms

Algorithm
egg-herbie
Counts
817 → 817
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0205617108
1500115587

prune1.4s

Pruning

11 alts after pruning (7 fresh and 4 done)

Merged error: 3.5b

regimes248.0ms

Accuracy

31.5% (8.5b remaining)

Error of 13.2b against oracle of 4.7b and baseline of 17.1b

bsearch103.0ms

Steps
ItersRangePoint
9
3.2605516108797835e+130
1.2684932886978702e+137
7.513255736758786e+136
10
-4.68496613899928e+225
-6.299496552493713e+213
-6.40315436234457e+213

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02412
12512
22512

end0.0ms

sample984.0ms

Algorithm
intervals
Results
767.0ms8429×body80valid