Details

Time bar (total: 8.2s)

sample38.0ms

Algorithm
intervals
Results
9.0ms201×body80valid
6.0ms256×pre80true
5.0ms26×body640valid
2.0ms10×body1280valid
2.0ms14×body320valid
0.0ms5×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 26.8b

Counts
2 → 1

localize16.0ms

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))
1.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite75.0ms

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:
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series577.0ms

Counts
3 → 9
Calls
3 calls:
223.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
278.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
75.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07011971
137401800
250011782

prune495.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New15414168
Fresh000
Picked101
Done000
Total15514169

Merged error: 6.9b

Counts
169 → 14

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
13.2b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite39.0ms

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:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series681.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
156.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
451.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify99.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07273112
132592892
250022876

prune508.0ms

Filtered
190 candidates to 135 candidates (71.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New1846190
Fresh4913
Picked101
Done000
Total18915204

Merged error: 6.9b

Counts
204 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ beta (+ alpha (+ beta (fma i 2.0 2.0))))
0.0b
(/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
0.1b
(/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
13.2b
(fma (/ (/ (+ alpha beta) 1) 1) (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
270×*-un-lft-identity
261×times-frac
130×add-sqr-sqrt add-cube-cbrt
84×distribute-lft-out
45×associate-/l*
18×associate-/r/
16×add-exp-log add-cbrt-cube
11×associate-/r* div-inv
9×flip3-+ flip-+
7×cbrt-undiv div-exp
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-/l/
1×fma-udef
Counts
4 → 257
Calls
4 calls:
7.0ms
(/ beta (+ alpha (+ beta (fma i 2.0 2.0))))
11.0ms
(/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
11.0ms
(/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) 1.0)

series774.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(/ beta (+ alpha (+ beta (fma i 2.0 2.0))))
185.0ms
(/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
182.0ms
(/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
337.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify111.0ms

Algorithm
egg-herbie
Counts
269 → 269
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
08373528
134803361
250013355

prune774.0ms

Filtered
269 candidates to 182 candidates (67.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2672269
Fresh31114
Picked101
Done000
Total27113284

Merged error: 6.9b

Counts
284 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
0.1b
(/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
3.2b
(* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta))
3.3b
(+ (* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) 1.0)

rewrite379.0ms

Algorithm
rewrite-expression-head
Rules
456×*-un-lft-identity
420×times-frac
196×add-sqr-sqrt
158×add-cube-cbrt
127×distribute-lft-out
59×associate-*l*
42×associate-/l*
37×distribute-lft-out--
28×associate-/r/
20×flip3-+ flip-+
18×div-inv
16×add-exp-log add-cbrt-cube
10×distribute-rgt-out--
9×difference-of-squares
8×frac-times
6×pow1 cbrt-undiv div-exp associate-/r* add-log-exp
4×expm1-log1p-u associate-*r* associate-*l/ log1p-expm1-u
3×flip3-- frac-sub flip-- sub-div
2×distribute-rgt-in associate-+l+ frac-2neg distribute-lft-in associate-*r/ clear-num associate-/l/
1×+-commutative fma-def pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 317
Calls
4 calls:
11.0ms
(/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
11.0ms
(/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
169.0ms
(* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta))
167.0ms
(+ (* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) 1.0)

series923.0ms

Counts
4 → 12
Calls
4 calls:
181.0ms
(/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
181.0ms
(/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))
334.0ms
(* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta))
227.0ms
(+ (* (- (/ (/ beta (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta))) (/ (/ alpha (+ alpha (+ beta (fma i 2.0 2.0)))) (fma i 2.0 (+ alpha beta)))) (+ alpha beta)) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014305379
150015235

prune854.0ms

Filtered
329 candidates to 222 candidates (67.5%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New3263329
Fresh21012
Picked011
Done000
Total32814342

Merged error: 6.9b

Counts
342 → 14

regimes323.0ms

Accuracy

-15.3% (7.3b remaining)

Error of 13.2b against oracle of 5.9b and baseline of 12.2b

bsearch254.0ms

Steps
ItersRangePoint
8
4.159463782749187e+169
5.4559085496255395e+172
4.22071431264922e+169
3
3.5396483413583083e+121
4.564372307405329e+121
4.4633300930535925e+121
9
3.0913287368252973e+102
1.8855737828649022e+108
3.974400637966621e+102
9
1.1149368389194534e+43
9.682444824959816e+51
9.509300076063801e+51

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07275
17675
27675

end0.0ms

sample978.0ms

Algorithm
intervals
Results
302.0ms6371×body80valid
172.0ms8000×pre80true
130.0ms539×body1280valid
111.0ms584×body640valid
46.0ms336×body320valid
18.0ms170×body160valid