Details

Time bar (total: 4.9s)

sample41.0ms

Algorithm
intervals
Results
12.0ms209×body80valid
5.0ms256×pre80true
5.0ms16×body1280valid
3.0ms12×body640valid
2.0ms10×body320valid
1.0ms9×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
0497027
1497027

prune8.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 11.1b

Counts
2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
2.0b
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)
2.6b
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

rewrite68.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
23×add-sqr-sqrt
17×add-cube-cbrt times-frac
15×flip3-+ flip-+
13×add-exp-log add-cbrt-cube
10×associate-/r/
8×frac-times associate-/l*
7×distribute-lft-out
6×pow1 add-log-exp
5×associate-/r*
4×associate-*r/ associate-*r* associate-*l* associate-*l/ associate-/l/
3×cbrt-undiv div-exp
2×frac-2neg div-sub prod-exp clear-num cbrt-unprod div-inv distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in associate-+l- flip3-- distribute-lft-in pow-prod-down sum-log *-commutative flip-- unswap-sqr
Counts
4 → 114
Calls
4 calls:
7.0ms
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
17.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
22.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)
19.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ (+ 2.0 (* 2.0 i)) (+ alpha beta))
23.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
93.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))) 1.0)
189.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
052752819

prune277.0ms

Filtered
100 candidates to 126 candidates (-26.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11412126
Fresh000
Picked101
Done000
Total11512127

Merged error: 10.5b

Counts
127 → 12

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
1.2b
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
1.5b
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
2.0b
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
18×flip3-+ flip-+
16×add-exp-log *-un-lft-identity associate-/r/ add-cbrt-cube
14×add-sqr-sqrt
12×frac-times
10×add-cube-cbrt
6×pow1 times-frac associate-*r/ associate-*l/ associate-/l* add-log-exp
4×cbrt-undiv div-exp associate-*r* associate-*l*
3×prod-exp cbrt-unprod
2×frac-2neg clear-num associate-/r* div-inv distribute-lft-out
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in diff-log pow-prod-down *-commutative flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 102
Calls
4 calls:
17.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
17.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
16.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
22.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

series151.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i))))
34.0ms
(/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
35.0ms
(/ beta (* (+ (/ (+ 2.0 (* 2.0 i)) (+ alpha beta)) 1) (+ alpha (+ beta (* 2.0 i)))))
59.0ms
(- (/ alpha (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)

simplify54.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
051372806

prune317.0ms

Filtered
92 candidates to 114 candidates (-23.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1095114
Fresh4711
Picked101
Done000
Total11412126

Merged error: 4.3b

Counts
126 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
0.3b
(/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
2.4b
(* (- beta alpha) (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))))
3.9b
(+ (* (- beta alpha) (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))) 1.0)

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
36×add-exp-log
20×add-cbrt-cube
19×flip3-+ associate-*r* flip-+
17×add-sqr-sqrt *-un-lft-identity
16×associate-/r/
14×frac-times prod-exp
11×pow1 add-cube-cbrt
9×associate-*l*
8×div-exp associate-*l/
7×associate-*r/
6×times-frac cbrt-unprod add-log-exp
4×cbrt-undiv rec-exp 1-exp
3×pow-prod-down associate-/l*
2×flip3-- pow-flip *-commutative flip-- div-inv distribute-lft-out unswap-sqr
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in clear-num associate-/r* sum-log un-div-inv distribute-lft-out-- inv-pow difference-of-squares
Counts
4 → 123
Calls
4 calls:
21.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
17.0ms
(/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
23.0ms
(* (- beta alpha) (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))))
21.0ms
(+ (* (- beta alpha) (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))) 1.0)

series362.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
63.0ms
(/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))
183.0ms
(* (- beta alpha) (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))))
92.0ms
(+ (* (- beta alpha) (/ 1 (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))) 1.0)

simplify45.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
049763247
149763247

prune462.0ms

Filtered
98 candidates to 135 candidates (-37.8%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1323135
Fresh2911
Picked101
Done000
Total13512147

Merged error: 4.3b

Counts
147 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
2.0b
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)
2.0b
(log (exp (+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)))
2.6b
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×add-sqr-sqrt
13×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×add-cube-cbrt
8×frac-times associate-/r/
7×pow1
6×add-log-exp
5×times-frac log-pow associate-/l*
4×log-prod exp-prod associate-*r/ associate-*r* associate-*l* associate-*l/ distribute-lft-out
3×div-sub
2×cbrt-undiv associate-+l- div-exp prod-exp cbrt-unprod associate-/l/ distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in log-div flip3-- frac-2neg distribute-lft-in exp-diff rem-log-exp exp-sum pow-prod-down clear-num associate-/r* sum-log *-commutative flip-- div-inv unswap-sqr
Counts
4 → 97
Calls
4 calls:
17.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
26.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)
23.0ms
(log (exp (+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)))
19.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))
92.0ms
(+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)
93.0ms
(log (exp (+ (/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i))))) 1.0)))
185.0ms
(/ (- beta alpha) (* (+ (/ (+ 2.0 (* 2.0 i)) (+ beta alpha)) 1) (+ beta (+ alpha (* 2.0 i)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049762887
149762887

prune208.0ms

Filtered
84 candidates to 109 candidates (-29.8%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1072109
Fresh11011
Picked011
Done000
Total10813121

Merged error: 4.3b

Counts
121 → 13

regimes401.0ms

Accuracy

17% (5.5b remaining)

Error of 11.0b against oracle of 5.5b and baseline of 12.2b

bsearch82.0ms

Steps
ItersRangePoint
8
4.6638125044168234e+172
3.901760339415494e+175
3.310133703349808e+173
9
3.859228315889123e+28
1.1261076737327934e+34
4.107849568665423e+28
7
22921240710501256.0
2.7895973467809126e+18
8.349129565153372e+17

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
071156
171156

end0.0ms

sample1.2s

Algorithm
intervals
Results
361.0ms6378×body80valid
166.0ms8000×pre80true
148.0ms509×body1280valid
126.0ms567×body640valid
55.0ms334×body320valid
23.0ms212×body160valid

Profiling

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