Details

Time bar (total: 9.1s)

sample37.0ms

Algorithm
intervals
Results
8.0ms205×body80valid
7.0ms256×pre80true
4.0ms21×body1280valid
3.0ms18×body640valid
1.0ms9×body320valid
0.0ms3×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.6b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.9b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.7b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite877.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
178.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
635.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
56.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series543.0ms

Counts
3 → 9
Calls
3 calls:
216.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
257.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
69.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify97.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune493.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
12.3b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite237.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-exp-log add-cbrt-cube
7×flip3-+ associate-/r* flip-+ div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-- flip-- fma-udef
Counts
3 → 181
Calls
3 calls:
45.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
182.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series469.0ms

Counts
3 → 9
Calls
3 calls:
71.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
150.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
248.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07273112
132592892
250022876

prune564.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
0.1b
(/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i)))
0.1b
(* (/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
12.3b
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite508.0ms

Algorithm
rewrite-expression-head
Rules
255×times-frac
196×add-sqr-sqrt
181×*-un-lft-identity
125×add-cube-cbrt
63×associate-*l*
32×add-exp-log add-cbrt-cube
25×distribute-lft-out-- difference-of-squares
24×associate-/l*
18×associate-*r*
13×cbrt-undiv div-exp
11×div-inv
6×pow1 prod-exp associate-/r* associate-/r/ cbrt-unprod unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×flip3-- div-sub flip-- associate-/l/ distribute-lft-out
2×frac-2neg clear-num
1×frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+ fma-udef
Counts
4 → 262
Calls
4 calls:
17.0ms
(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
51.0ms
(/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i)))
426.0ms
(* (/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series556.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
86.0ms
(/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i)))
153.0ms
(* (/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
250.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (* (/ (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) (- (+ alpha beta) (* 2.0 i))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify72.0ms

Algorithm
egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012314683
150014244

prune987.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.3b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
12.1b
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite397.0ms

Algorithm
rewrite-expression-head
Rules
490×times-frac
410×*-un-lft-identity
284×add-sqr-sqrt
228×add-cube-cbrt
156×sqrt-prod
63×distribute-lft-out
42×associate-/l*
28×distribute-lft-out-- difference-of-squares
22×associate-/r/
19×div-inv
18×add-exp-log
17×associate-/r*
16×add-cbrt-cube
11×flip3-+ flip-+
9×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u sqrt-div log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg div-sub clear-num
1×flip3-- 1-exp flip-- fma-udef
Counts
4 → 402
Calls
4 calls:
45.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
142.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
186.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series637.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
127.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
209.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
226.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify98.0ms

Algorithm
egg-herbie
Counts
414 → 414
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012837520
150016992

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.2b

regimes178.0ms

Accuracy

19.4% (5.4b remaining)

Error of 11.1b against oracle of 5.7b and baseline of 12.5b

bsearch166.0ms

Steps
ItersRangePoint
6
2.3275081152992616e+225
3.277662341302102e+226
2.7243108990955635e+225
4
6.928579214014599e+217
1.006338786594451e+218
8.42223840336915e+217
9
1.8714686899322058e+171
4.019695394184786e+177
6.749629698172741e+176

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06667
16867
26867

end0.0ms

sample838.0ms

Algorithm
intervals
Results
261.0ms6380×body80valid
110.0ms8000×pre80true
99.0ms532×body1280valid
84.0ms567×body640valid
36.0ms323×body320valid
15.0ms198×body160valid