Details

Time bar (total: 10.8s)

sample32.0ms

Algorithm
intervals
Results
8.0ms204×body80valid
4.0ms256×pre80true
3.0ms17×body1280valid
3.0ms20×body640valid
1.0ms12×body320valid
0.0ms3×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

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: 24.6b

Counts
2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.8b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
54×*-un-lft-identity times-frac
32×add-sqr-sqrt
28×add-cube-cbrt
20×add-exp-log add-cbrt-cube
14×flip3-+ associate-/r/ flip-+
12×distribute-lft-out
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r* div-inv
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×associate-*r/ associate-*l* associate-*l/
3×prod-exp cbrt-unprod
2×distribute-rgt-in sub-neg frac-2neg distribute-lft-in clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 144
Calls
4 calls:
9.0ms
(* (+ alpha beta) (- beta alpha))
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
29.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series631.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (+ alpha beta) (- beta alpha))
231.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
82.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify122.0ms

Algorithm
egg-herbie
Counts
156 → 156
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07672103
143531976
250031976

prune433.0ms

Filtered
156 candidates to 112 candidates (71.8%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1479156
Fresh000
Picked101
Done000
Total1489157

Merged error: 5.3b

Counts
157 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
45×add-sqr-sqrt
35×times-frac
26×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
8×flip3-+ flip-+
7×associate-/r* associate-/l/ distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r/ associate-/l* add-log-exp
4×frac-times associate-*l* associate-*l/ prod-exp cbrt-unprod distribute-lft-out
3×div-inv
2×frac-2neg associate-*r/ clear-num unswap-sqr
1×+-commutative flip3-- div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 129
Calls
4 calls:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
22.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series663.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
230.0ms
(/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
279.0ms
(+ (/ (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify94.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
06571569
135541429
250011429

prune379.0ms

Filtered
141 candidates to 101 candidates (71.6%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1338141
Fresh718
Picked101
Done000
Total1419150

Merged error: 5.3b

Counts
150 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
0.2b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
0.8b
(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite100.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
61×*-un-lft-identity
52×add-exp-log
49×add-sqr-sqrt
38×add-cube-cbrt
32×add-cbrt-cube
28×associate-/r/
25×div-exp
21×associate-*r*
15×flip3-+ flip-+
14×associate-/r*
13×cbrt-undiv
12×frac-times associate-*l/
10×prod-exp
9×distribute-lft-out
8×div-inv
7×pow1 associate-/l*
6×associate-*r/ cbrt-unprod add-log-exp
4×rec-exp 1-exp associate-*l*
3×distribute-lft-out-- difference-of-squares
2×frac-2neg clear-num associate-/l/ unswap-sqr
1×+-commutative pow-flip pow-prod-down sum-log *-commutative inv-pow
Counts
4 → 174
Calls
4 calls:
16.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
22.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
21.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
34.0ms
(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series772.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
179.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))
231.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
279.0ms
(+ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify119.0ms

Algorithm
egg-herbie
Counts
186 → 186
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08372794
146112428
250012418

prune433.0ms

Filtered
186 candidates to 108 candidates (58.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1833186
Fresh268
Picked101
Done000
Total1869195

Merged error: 5.3b

Counts
195 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
0.2b
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
0.6b
(- 1.0 (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))
0.7b
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
82×*-un-lft-identity
72×add-exp-log
55×add-sqr-sqrt
48×add-cube-cbrt
42×associate-/r/
40×div-exp
32×add-cbrt-cube
26×associate-/r*
17×flip3-+ flip-+ distribute-lft-out
16×cbrt-undiv frac-times associate-*l/
15×div-inv
12×prod-exp
8×unpow-prod-down rec-exp 1-exp cube-prod associate-*r/ add-log-exp
6×pow1 associate-/l*
4×cbrt-unprod
3×difference-of-squares
2×pow-flip frac-2neg clear-num distribute-lft-out-- inv-pow
1×+-commutative sub-neg flip3-- diff-log sum-log sum-cubes flip--
Counts
4 → 206
Calls
4 calls:
22.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
22.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
21.0ms
(- 1.0 (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))
64.0ms
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))

series4.8s

Counts
4 → 12
Calls
4 calls:
231.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
235.0ms
(/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))
178.0ms
(- 1.0 (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))))
4.1s
(+ (pow (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (* (+ alpha beta) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))) 3) (pow 1.0 3))

simplify121.0ms

Algorithm
egg-herbie
Counts
218 → 218
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07123938
137073457
250023443

prune575.0ms

Filtered
218 candidates to 103 candidates (47.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2144218
Fresh268
Picked101
Done000
Total21710227

Merged error: 5.3b

Counts
227 → 10

regimes246.0ms

Accuracy

13.8% (5.5b remaining)

Error of 11.5b against oracle of 6.0b and baseline of 12.4b

bsearch93.0ms

Steps
ItersRangePoint
8
3.918843472614674e+137
1.0363106199006555e+140
7.328664447613938e+139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067108
167108

end0.0ms

sample818.0ms

Algorithm
intervals
Results
245.0ms6350×body80valid
139.0ms8000×pre80true
101.0ms518×body1280valid
87.0ms567×body640valid
41.0ms359×body320valid
18.0ms206×body160valid