Details

Time bar (total: 6.1s)

sample45.0ms

Algorithm
intervals
Results
10.0ms195×body80valid
6.0ms22×body1280valid
6.0ms256×pre80true
4.0ms17×body640valid
2.0ms14×body320valid
1.0ms8×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.4b

Counts
2 → 1

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))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
19.0ms
(/ (/ (* (+ 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)
13.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series162.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify95.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250011789

prune255.0ms

Filtered
89 candidates to 120 candidates (-34.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New11010120
Fresh000
Picked101
Done000
Total11110121

Merged error: 5.7b

Counts
121 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
0.3b
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
1.6b
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite233.0ms

Algorithm
rewrite-expression-head
Rules
1250×times-frac
1055×*-un-lft-identity
619×add-sqr-sqrt
461×add-cube-cbrt
218×distribute-lft-out
96×associate-/l*
79×distribute-lft-out-- difference-of-squares
60×associate-/r/
33×div-inv
30×associate-/r*
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 645
Calls
4 calls:
36.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
11.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
117.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series190.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
17.0ms
(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha)))
19.0ms
(/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))
89.0ms
(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2.0 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify159.0ms

Algorithm
egg-herbie
Counts
657 → 657
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0178313720
1500113481

prune1.2s

Filtered
362 candidates to 657 candidates (-81.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New6516657
Fresh459
Picked101
Done000
Total65611667

Merged error: 5.7b

Counts
667 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.7b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
321×times-frac
290×*-un-lft-identity
211×add-sqr-sqrt
140×add-cube-cbrt
90×associate-*r*
44×distribute-lft-out
31×distribute-lft-out-- difference-of-squares
26×associate-/l*
24×associate-/r/
20×add-exp-log add-cbrt-cube
15×flip3-+ flip-+
12×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×associate-*l*
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 295
Calls
4 calls:
20.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
41.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
25.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series205.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
65.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
85.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify70.0ms

Algorithm
egg-herbie
Counts
307 → 307
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010834781
150014605

prune552.0ms

Filtered
202 candidates to 307 candidates (-52.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3043307
Fresh3710
Picked101
Done000
Total30810318

Merged error: 5.7b

Counts
318 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.7b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.0b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
4.1b
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
162×times-frac
151×*-un-lft-identity
116×add-sqr-sqrt
90×associate-*r*
75×add-cube-cbrt
22×distribute-lft-out
16×distribute-lft-out-- difference-of-squares
15×add-exp-log add-cbrt-cube
12×associate-/r/
9×flip3-+ flip-+
7×pow1
6×div-inv add-log-exp
5×associate-/l*
4×cbrt-undiv log-prod div-exp associate-*l* log-pow
3×exp-prod prod-exp associate-/r* cbrt-unprod unswap-sqr
2×frac-times associate-*l/ associate-/l/
1×+-commutative flip3-- frac-2neg div-sub associate-*r/ rem-log-exp exp-sum pow-prod-down clear-num sum-log *-commutative flip--
Counts
4 → 184
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
43.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
26.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
28.0ms
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
65.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
82.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
85.0ms
(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09222625
150012462

prune570.0ms

Filtered
132 candidates to 196 candidates (-48.5%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1951196
Fresh099
Picked011
Done000
Total19511206

Merged error: 5.6b

Counts
206 → 11

regimes535.0ms

Accuracy

76.4% (1.6b remaining)

Error of 7.5b against oracle of 6.0b and baseline of 12.6b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05239
15239

end0.0ms

sample1.2s

Algorithm
intervals
Results
352.0ms6323×body80valid
175.0ms8000×pre80true
152.0ms525×body1280valid
127.0ms577×body640valid
66.0ms382×body320valid
21.0ms193×body160valid

Profiling

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