Details

Time bar (total: 4.3s)

sample19.0ms

Algorithm
intervals
Results
9.0ms273×body80valid

simplify12.0ms

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: 29.2b

localize9.0ms

Local error

Found 2 expressions with local error:

0.2b
(- (* b c) (* a d))
28.7b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/
1×cbrt-undiv sub-neg frac-2neg flip3-+ fma-neg diff-log div-sub div-exp prod-diff clear-num flip-+ div-inv
Counts
2 → 50
Calls
2 calls:
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series121.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(- (* b c) (* a d))
84.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify105.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (97.0ms)

IterNodesCost
0268481
11010432
23840422
35001421

prune157.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 13.6b

localize13.0ms

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)))
17.3b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite42.0ms

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))

series392.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(/ 1 (* (hypot c d) 1))
38.0ms
(- (* b c) (* a d))
182.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
116.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05531207
123041003
25001995

prune360.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

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))
17.3b
(/ (- (* 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))

series272.0ms

Counts
3 → 9
Calls
3 calls:
117.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
41.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify52.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04491408
116571307
250011298

prune382.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize12.0ms

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))))
0.2b
(- (* b c) (* a d))
17.4b
(/ (hypot c d) (- (* b c) (* a d)))

rewrite62.0ms

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:
24.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
9.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
3.0ms
(- (* b c) (* a d))
5.0ms
(/ (hypot c d) (- (* b c) (* a d)))

series418.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (/ 1 (/ (hypot c d) (- (* b c) (* a d)))) (hypot c d))
113.0ms
(/ 1 (/ (hypot c d) (- (* b c) (* a d))))
38.0ms
(- (* b c) (* a d))
93.0ms
(/ (hypot c d) (- (* b c) (* a d)))

simplify72.0ms

Algorithm
egg-herbie
Counts
371 → 371
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012945404
150024894

prune904.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.4b

regimes215.0ms

Accuracy

29.2% (9.0b remaining)

Error of 13.6b against oracle of 4.6b and baseline of 17.3b

bsearch78.0ms

Steps
ItersRangePoint
8
5.265695259277909e+173
7.825150772293386e+177
1.5910699936696656e+174
9
-1.085810015494438e+65
-1.2809166914199238e+60
-1.0689057415946615e+65

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03015
13115
23115

end0.0ms

sample530.0ms

Algorithm
intervals
Results
310.0ms8485×body80valid