Details

Time bar (total: 55.0s)

sample42.0ms

Algorithm
intervals
Results
9.0ms189×body80valid
6.0ms256×pre80true
5.0ms20×body1280valid
4.0ms21×body640valid
3.0ms20×body320valid
1.0ms6×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

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: 27.9b

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))
1.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.4b
(/ (* (+ 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:
19.0ms
(/ (/ (* (+ 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)))

series582.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
277.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
77.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
07011971
137401800
250011782

prune489.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1599168
Fresh000
Picked101
Done000
Total1609169

Merged error: 7.4b

Counts
169 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.1b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
3.5b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3236
Calls
4 calls:
11.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
84.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
28.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
553.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series626.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
293.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
148.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
120.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify494.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500147178

prune8.1s

Filtered
3248 candidates to 1754 candidates (54.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New3238103248
Fresh628
Picked101
Done000
Total3245123257

Merged error: 7.3b

Counts
3257 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.3b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
2.9b
(- (* 1.0 1.0) (* (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
3.5b
(+ (pow (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
10024×times-frac
6745×*-un-lft-identity
4603×add-sqr-sqrt
3451×add-cube-cbrt
2362×fma-def
1182×unpow-prod-down cube-prod
1071×distribute-lft-out
576×distribute-lft-out-- difference-of-squares
398×associate-/r/
204×div-inv
192×associate-/r*
163×flip3-+ flip-+
46×add-exp-log
33×flip3-- flip--
30×div-exp
22×add-cbrt-cube
12×cbrt-undiv
8×add-log-exp
6×pow1 rec-exp 1-exp associate-/l*
4×expm1-log1p-u log1p-expm1-u
2×pow-flip frac-2neg clear-num inv-pow
1×+-commutative cube-mult sub-neg distribute-rgt-out-- fma-neg diff-log unpow3 prod-diff sum-log sum-cubes sqr-pow
Counts
4 → 3226
Calls
4 calls:
25.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
28.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
4.0ms
(- (* 1.0 1.0) (* (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
1.5s
(+ (pow (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

series20.9s

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
142.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
122.0ms
(- (* 1.0 1.0) (* (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))
20.5s
(+ (pow (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 3) (pow 1.0 3))

simplify209.0ms

Algorithm
egg-herbie
Counts
3238 → 3238
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0172413971
1500113175

prune8.0s

Filtered
3238 candidates to 1047 candidates (32.3%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New323263238
Fresh11011
Picked101
Done000
Total3234163250

Merged error: 7.3b

Counts
3250 → 16

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.3b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
15.6b
(fma (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite523.0ms

Algorithm
rewrite-expression-head
Rules
8864×times-frac
5577×*-un-lft-identity
4141×add-sqr-sqrt
3133×add-cube-cbrt
1192×sqrt-prod
718×distribute-lft-out
504×distribute-lft-out-- difference-of-squares
349×associate-/r/
299×associate-/l*
179×div-inv
142×flip3-+ flip-+
110×associate-/r*
61×add-exp-log
42×div-exp
29×add-cbrt-cube
28×flip3-- flip--
17×cbrt-undiv
7×pow1 rec-exp 1-exp
4×expm1-log1p-u pow-flip sqrt-div log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×inv-pow
1×sqrt-pow1 pow1/2 fma-udef associate-/l/
Counts
4 → 2857
Calls
4 calls:
32.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
101.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
15.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.0ms
(fma (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series809.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
310.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
130.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
223.0ms
(fma (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify747.0ms

Algorithm
egg-herbie
Counts
2869 → 2869
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
0500178194

prune7.9s

Filtered
2869 candidates to 1459 candidates (50.9%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New286812869
Fresh01515
Picked101
Done000
Total2869162885

Merged error: 7.3b

Counts
2885 → 16

regimes482.0ms

Accuracy

9.3% (6.0b remaining)

Error of 12.0b against oracle of 6.0b and baseline of 12.6b

bsearch227.0ms

Steps
ItersRangePoint
8
1.7863704641000046e+190
6.112994386879021e+194
1.278754787491978e+191
10
5.5953080499269384e+135
5.48548194170192e+146
7.135141287374778e+135
6
5.220524812885973e+61
2.6275011625717387e+62
2.5911491888942357e+62

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
05150
15625
25925
35925

end0.0ms

sample1.2s

Algorithm
intervals
Results
512.0ms6329×body80valid
179.0ms8000×pre80true
130.0ms520×body1280valid
114.0ms576×body640valid
55.0ms374×body320valid
20.0ms201×body160valid