Details

Time bar (total: 24.7s)

sample48.0ms

Algorithm
intervals
Results
16.0ms207×body80valid
6.0ms256×pre80true
6.0ms15×body1280valid
4.0ms15×body640valid
3.0ms13×body320valid
1.0ms6×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.6b

localize13.0ms

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))
1.9b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.4b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite462.0ms

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:
90.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
334.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
30.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series576.0ms

Counts
3 → 9
Calls
3 calls:
222.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
273.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune533.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 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))
0.8b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
3.8b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.6s

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:
163.0ms
(/ (/ 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))
28.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series618.0ms

Counts
4 → 12
Calls
4 calls:
288.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
67.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
146.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
118.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify474.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500147178

prune9.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (- beta alpha))
0.5b
(cbrt (- beta alpha))
0.6b
(/ 1 (/ (/ (cbrt (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (cbrt (- beta alpha))))
11.6b
(fma (/ (/ 1 (/ (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) 1) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ 1 (/ (/ (cbrt (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (cbrt (- beta alpha)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
2466×times-frac
1605×*-un-lft-identity
1221×add-sqr-sqrt
994×cbrt-prod
977×add-cube-cbrt
246×associate-/r*
192×distribute-lft-out
122×distribute-lft-out-- difference-of-squares
73×associate-/r/
37×div-inv
32×flip3-+ flip-+
25×add-exp-log
15×div-exp
12×cbrt-div
10×add-cbrt-cube
6×cbrt-undiv flip3-- flip--
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp 1-exp associate-/l*
2×pow1/3
1×pow-flip frac-2neg clear-num fma-udef inv-pow
Counts
4 → 1058
Calls
4 calls:
2.0ms
(cbrt (- beta alpha))
2.0ms
(cbrt (- beta alpha))
58.0ms
(/ 1 (/ (/ (cbrt (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (cbrt (- beta alpha))))
0.0ms
(fma (/ (/ 1 (/ (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) 1) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ 1 (/ (/ (cbrt (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (cbrt (- beta alpha)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series2.4s

Counts
4 → 12
Calls
4 calls:
150.0ms
(cbrt (- beta alpha))
153.0ms
(cbrt (- beta alpha))
158.0ms
(/ 1 (/ (/ (cbrt (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (cbrt (- beta alpha))))
2.0s
(fma (/ (/ 1 (/ (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) 1) (* (cbrt (- beta alpha)) (cbrt (- beta alpha))))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ 1 (/ (/ (cbrt (fma i 2.0 (+ alpha beta))) (+ alpha beta)) (cbrt (- beta alpha)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify243.0ms

Algorithm
egg-herbie
Counts
1070 → 1070
Iterations

Useful iterations: 1 (53.0ms)

IterNodesCost
0320021487
1500120642

prune4.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.8b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
11.9b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite94.0ms

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/
33×div-inv
32×add-exp-log
27×flip3-+ flip-+
24×associate-/l*
20×add-cbrt-cube
19×div-exp
10×cbrt-undiv
5×pow1 flip3-- flip--
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp frac-2neg 1-exp clear-num
1×pow-flip fma-udef associate-/l/ inv-pow
Counts
4 → 591
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
19.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
28.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series353.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
69.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
152.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
83.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify120.0ms

Algorithm
egg-herbie
Counts
603 → 603
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
016358750
150028070

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.6b

regimes248.0ms

Accuracy

5.1% (6.1b remaining)

Error of 12.0b against oracle of 5.9b and baseline of 12.3b

bsearch79.0ms

Steps
ItersRangePoint
8
5.6392287225097694e+57
3.6667847887492325e+62
3.602563790703159e+62

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
14526

end0.0ms

sample1.3s

Algorithm
intervals
Results
495.0ms6376×body80valid
185.0ms508×body1280valid
174.0ms8000×pre80true
169.0ms573×body640valid
79.0ms356×body320valid
28.0ms187×body160valid