Details

Time bar (total: 16.3s)

sample33.0ms

Algorithm
intervals
Results
8.0ms204×body80valid
4.0ms256×pre80true
3.0ms14×body1280valid
2.0ms20×body320valid
2.0ms14×body640valid
0.0ms4×body160valid

simplify55.0ms

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: 24.8b

Counts
2 → 1

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ 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)
20.4b
(/ (* (+ 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:
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
15.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series580.0ms

Counts
3 → 9
Calls
3 calls:
224.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
272.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
83.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify99.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07011971
137401800
250011782

prune487.0ms

Filtered
168 candidates to 131 candidates (78.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1608168
Fresh000
Picked101
Done000
Total1618169

Merged error: 5.8b

Counts
169 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.2b
(/ 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)

rewrite998.0ms

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:
89.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
27.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
428.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series632.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
68.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
151.0ms
(/ 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)

simplify501.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500147194

prune8.1s

Filtered
3248 candidates to 1754 candidates (54.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New323993248
Fresh527
Picked101
Done000
Total3245113256

Merged error: 5.8b

Counts
3256 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.2b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
12.4b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
1062×times-frac
759×*-un-lft-identity
595×add-sqr-sqrt
413×add-cube-cbrt
105×associate-/r*
91×distribute-lft-out-- difference-of-squares
82×distribute-lft-out
65×associate-/r/
34×add-exp-log
33×div-inv
27×flip3-+ flip-+
24×associate-/l*
20×div-exp add-cbrt-cube
10×cbrt-undiv
6×pow1
5×flip3-- flip--
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-flip inv-pow
1×fma-udef associate-/l/
Counts
4 → 595
Calls
4 calls:
9.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
12.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
26.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series360.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
62.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
150.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
84.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify133.0ms

Algorithm
egg-herbie
Counts
607 → 607
Iterations

Useful iterations: 1 (41.0ms)

IterNodesCost
017428804
150018301

prune1.4s

Filtered
607 candidates to 323 candidates (53.2%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New6043607
Fresh1910
Picked101
Done000
Total60612618

Merged error: 5.8b

Counts
618 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))))
0.3b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.3b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
7.2b
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))) 1.0)

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
87×add-exp-log
77×times-frac
70×add-sqr-sqrt
54×add-cube-cbrt
52×sqrt-prod
49×add-cbrt-cube
36×prod-exp
29×div-exp
27×associate-*l*
18×cbrt-unprod
15×cbrt-undiv
14×associate-/r*
13×distribute-lft-out
11×pow1
8×associate-/l* distribute-lft-out-- difference-of-squares
6×rec-exp sqrt-div 1-exp associate-/r/ add-log-exp
5×frac-times associate-*r/
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×pow-flip pow-prod-down associate-*l/ div-inv
2×frac-2neg clear-num associate-/l/
1×+-commutative flip3-- fma-def sqrt-pow1 pow1/2 div-sub associate-*r* sum-log *-commutative flip-- inv-pow
Counts
4 → 210
Calls
4 calls:
39.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))))
11.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
33.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))) 1.0)

series765.0ms

Counts
4 → 12
Calls
4 calls:
233.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))))
120.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
133.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
279.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))) 1.0)

simplify127.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
09503691
149253156
250013155

prune471.0ms

Filtered
222 candidates to 122 candidates (55.0%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New2211222
Fresh01111
Picked011
Done000
Total22113234

Merged error: 5.8b

Counts
234 → 13

regimes226.0ms

Accuracy

0.1% (6.4b remaining)

Error of 12.6b against oracle of 6.2b and baseline of 12.6b

bsearch80.0ms

Steps
ItersRangePoint
9
2.328261958232743e+54
1.864398490589349e+59
4.4350244846890366e+58

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample864.0ms

Algorithm
intervals
Results
264.0ms6331×body80valid
132.0ms8000×pre80true
117.0ms528×body1280valid
96.0ms579×body640valid
49.0ms382×body320valid
15.0ms180×body160valid