Details

Time bar (total: 3.7s)

sample20.0ms

Algorithm
intervals
Results
10.0ms269×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b
(- (* b c) (* a d))
25.6b
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite13.0ms

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:
4.0ms
(- (* b c) (* a d))
8.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series127.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(- (* b c) (* a d))
89.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify107.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 3 (101.0ms)

IterNodesCost
0268481
11010432
23840422
35001421

prune161.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

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)))
0.7b
(- (* b c) (* a d))
17.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite35.0ms

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))
13.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series399.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ 1 (* (hypot c d) 1))
186.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
118.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify65.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05531207
123041003
25001995

prune338.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.7b
(- (* b c) (* a d))
17.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite22.0ms

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:
8.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series280.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
39.0ms
(- (* b c) (* a d))
123.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify59.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04491408
116571307
250011298

prune386.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.3b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.7b
(- (* b c) (* a d))
17.4b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg pow-flip fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 139
Calls
4 calls:
3.0ms
(/ 1 (hypot c d))
15.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
4.0ms
(- (* b c) (* a d))
6.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series391.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 1 (hypot c d))
186.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
116.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify61.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04901189
122601039
250011009

prune368.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.7b

regimes199.0ms

Accuracy

32% (8.2b remaining)

Error of 13.2b against oracle of 4.9b and baseline of 17.0b

bsearch88.0ms

Steps
ItersRangePoint
9
1.9863725059419476e+127
2.650660898037378e+133
7.04631729015775e+128
10
-1.2626370227035731e+107
-2.5015671139411194e+96
-1.2498976234817265e+107

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03216
13316
23316

end0.0ms

sample523.0ms

Algorithm
intervals
Results
314.0ms8467×body80valid