Details

Time bar (total: 12.6s)

sample33.0ms

Algorithm
intervals
Results
7.0ms193×body80valid
4.0ms256×pre80true
4.0ms19×body1280valid
3.0ms22×body640valid
2.0ms14×body320valid
1.0ms8×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 26.8b

Counts
2 → 1

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))
2.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.5b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite716.0ms

Algorithm
rewrite-expression-head
Rules
7702×*-un-lft-identity
4214×distribute-lft-out
3666×times-frac
1502×associate-*l*
1412×add-sqr-sqrt
900×add-cube-cbrt
894×fma-def
640×associate-*r*
141×associate-/l*
128×*-commutative distribute-lft-out-- difference-of-squares unswap-sqr
49×associate-/l/
40×associate-/r/
27×flip3-+ flip-+
22×associate-/r*
20×div-inv
17×add-exp-log add-cbrt-cube
8×frac-times
7×cbrt-undiv div-exp
6×flip3-- flip--
5×add-log-exp
4×associate-*r/ associate-*l/
3×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u
2×prod-exp cbrt-unprod
1×+-commutative sum-log
Counts
3 → 2121
Calls
3 calls:
69.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
330.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
23.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series643.0ms

Counts
3 → 9
Calls
3 calls:
246.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
303.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
93.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify277.0ms

Algorithm
egg-herbie
Counts
2130 → 2130
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0144421714
1500221211

prune1.4s

Filtered
2130 candidates to 411 candidates (19.3%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2115152130
Fresh000
Picked101
Done000
Total2116152131

Merged error: 6.2b

Counts
2131 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
0.1b
(* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
0.5b
(/ 1 (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))))
2.1b
(+ (/ 1 (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))) 1.0)

rewrite426.0ms

Algorithm
rewrite-expression-head
Rules
1973×*-un-lft-identity
850×distribute-lft-out
831×times-frac
775×add-sqr-sqrt
561×frac-times
515×add-cube-cbrt
487×associate-/r*
468×associate-/r/
459×associate-/l*
440×associate-*l*
425×fma-def
168×associate-*r*
95×clear-num
92×frac-2neg
82×distribute-lft-out-- difference-of-squares
72×associate-/l/
62×add-exp-log
51×associate-*l/
45×flip3-+ flip-+
36×add-cbrt-cube
33×associate-*r/
32×unswap-sqr
27×div-exp
20×div-inv
16×prod-exp
14×cbrt-undiv
9×pow1 flip3-- flip--
8×*-commutative cbrt-unprod
6×un-div-inv add-log-exp
5×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u
2×pow-flip pow-prod-down
1×+-commutative sum-log inv-pow
Counts
4 → 1305
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
47.0ms
(* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
67.0ms
(/ 1 (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))))
185.0ms
(+ (/ 1 (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))) 1.0)

series832.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
197.0ms
(* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
253.0ms
(/ 1 (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))))
303.0ms
(+ (/ 1 (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))) 1.0)

simplify184.0ms

Algorithm
egg-herbie
Counts
1317 → 1317
Iterations

Useful iterations: 1 (51.0ms)

IterNodesCost
0222412512
1500111997

prune2.6s

Filtered
1317 candidates to 632 candidates (48.0%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New130891317
Fresh9514
Picked011
Done000
Total1317151332

Merged error: 6.2b

Counts
1332 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
0.1b
(* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
0.1b
(/ (sqrt 1) (* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))))
14.9b
(fma (/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (sqrt 1) (* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))) 1.0)

rewrite130.0ms

Algorithm
rewrite-expression-head
Rules
587×add-sqr-sqrt times-frac
565×*-un-lft-identity
351×add-cube-cbrt
261×associate-/r*
220×frac-times
168×associate-*r*
167×associate-/r/
153×sqrt-prod
149×associate-/l*
144×associate-*l*
60×add-exp-log
50×clear-num distribute-lft-out-- difference-of-squares
48×frac-2neg distribute-lft-out unswap-sqr
36×add-cbrt-cube
26×div-exp
22×associate-*r/
20×associate-*l/
18×div-inv
16×prod-exp
14×cbrt-undiv
9×flip3-- flip--
8×flip3-+ *-commutative cbrt-unprod flip-+
6×pow1
4×expm1-log1p-u rec-exp 1-exp un-div-inv log1p-expm1-u add-log-exp
1×pow-prod-down fma-udef
Counts
4 → 765
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
23.0ms
(* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
45.0ms
(/ (sqrt 1) (* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))))
1.0ms
(fma (/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (sqrt 1) (* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))) 1.0)

series589.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
145.0ms
(* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
93.0ms
(/ (sqrt 1) (* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))))
271.0ms
(fma (/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (/ (sqrt 1) (* (/ 1 (+ alpha beta)) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))) 1.0)

simplify154.0ms

Algorithm
egg-herbie
Counts
777 → 777
Iterations

Useful iterations: 1 (52.0ms)

IterNodesCost
021149895
150018321

prune1.6s

Filtered
777 candidates to 371 candidates (47.7%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New7743777
Fresh21113
Picked101
Done011
Total77715792

Merged error: 6.2b

Counts
792 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b
(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
0.1b
(* (/ (+ alpha beta) 1) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))
14.9b
(fma (/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* 1 (* (/ (+ alpha beta) 1) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) 1.0)

rewrite73.0ms

Algorithm
rewrite-expression-head
Rules
301×*-un-lft-identity
167×add-sqr-sqrt
156×frac-times
134×associate-/l*
110×add-cube-cbrt
97×times-frac
94×distribute-lft-out
92×associate-/r*
56×associate-/l/
30×associate-*l* clear-num
29×frac-2neg
27×sqrt-prod
25×add-exp-log
21×distribute-lft-out--
20×add-cbrt-cube difference-of-squares
19×associate-*r*
15×flip3-+ flip-+
14×flip3-- flip--
13×associate-*r/
12×associate-*l/
9×div-exp
6×pow1 cbrt-undiv prod-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv add-log-exp
3×un-div-inv
2×1-exp associate-/r/
1×div-sub pow-prod-down *-commutative fma-udef
Counts
4 → 374
Calls
4 calls:
17.0ms
(/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms
(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
28.0ms
(* (/ (+ alpha beta) 1) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))
1.0ms
(fma (/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* 1 (* (/ (+ alpha beta) 1) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) 1.0)

series520.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
84.0ms
(/ (- beta alpha) (fma i 2.0 (+ alpha beta)))
92.0ms
(* (/ (+ alpha beta) 1) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))
276.0ms
(fma (/ (sqrt 1) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (* 1 (* (/ (+ alpha beta) 1) (/ (- beta alpha) (fma i 2.0 (+ alpha beta))))) 1.0)

simplify88.0ms

Algorithm
egg-herbie
Counts
386 → 386
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
014623787
150023431

prune820.0ms

Filtered
386 candidates to 206 candidates (53.4%)
Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New3851386
Fresh01313
Picked101
Done011
Total38615401

Merged error: 6.2b

Counts
401 → 15

regimes374.0ms

Accuracy

3.8% (6.5b remaining)

Error of 12.5b against oracle of 6.0b and baseline of 12.7b

bsearch177.0ms

Steps
ItersRangePoint
9
3.919704473779381e+257
5.196889498499753e+263
4.159005638992996e+257
3
6.098250721752438e+226
8.407082942025467e+226
7.974176900724274e+226
5
1.1027112679789028e+77
2.926579115410215e+77
2.779043914801437e+77

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
05758
16029
26329
36329

end0.0ms

sample836.0ms

Algorithm
intervals
Results
250.0ms6298×body80valid
128.0ms8000×pre80true
110.0ms541×body1280valid
96.0ms608×body640valid
46.0ms359×body320valid
18.0ms194×body160valid