Details

Time bar (total: 34.2s)

sample32.0ms

Algorithm
intervals
Results
14.0ms256×body80valid
5.0ms256×pre80true

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune13.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 51.6b

Counts
2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
40.6b
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
41.4b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
52×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp prod-exp cbrt-unprod
16×add-sqr-sqrt times-frac
13×add-cube-cbrt *-un-lft-identity
11×pow1
10×associate-*l/ associate-/r*
6×associate-*r*
5×associate-*l*
4×expm1-log1p-u pow-prod-down fma-udef log1p-expm1-u div-inv associate-/l/ add-log-exp
3×flip3-- flip--
2×distribute-rgt-in frac-2neg distribute-lft-in associate-*r/ clear-num *-commutative associate-/l*
1×flip3-+ associate-/r/ flip-+ difference-of-squares unswap-sqr
Counts
4 → 122
Calls
4 calls:
16.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
15.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
20.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
18.0ms
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series3.6s

Counts
4 → 12
Calls
4 calls:
505.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
266.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
918.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
1.9s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify51.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435

prune416.0ms

Filtered
134 candidates to 97 candidates (72.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1277134
Fresh011
Picked101
Done000
Total1288136

Merged error: 43.7b

Counts
136 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
7.6b
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
35.4b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
40.6b
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
61×add-exp-log add-cbrt-cube
47×add-sqr-sqrt
44×add-cube-cbrt *-un-lft-identity
34×associate-/r*
29×cbrt-undiv div-exp
12×prod-exp cbrt-unprod
9×div-inv
6×pow1
5×associate-/l*
4×expm1-log1p-u associate-*l* associate-*l/ associate-/r/ log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num
2×flip3-- associate-*r/ flip-- fma-udef
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down *-commutative flip-+ difference-of-squares unswap-sqr
Counts
4 → 176
Calls
4 calls:
16.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
19.0ms
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
23.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

series3.1s

Counts
4 → 12
Calls
4 calls:
272.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
1.9s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
123.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
768.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
09814480
150013634

prune542.0ms

Filtered
188 candidates to 139 candidates (73.9%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1844188
Fresh617
Picked101
Done000
Total1915196

Merged error: 34.9b

Counts
196 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
0.5b
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
35.4b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
38.1b
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
15593×times-frac
8400×*-un-lft-identity
6296×add-sqr-sqrt
5595×add-cube-cbrt
1683×distribute-lft-out
701×difference-of-squares
524×div-inv
411×associate-/r/
140×flip3-+ flip-+
93×associate-/l*
78×associate-/r*
49×add-exp-log add-cbrt-cube
32×cbrt-undiv div-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
3×associate-/l/
1×flip3-- div-sub flip--
Counts
4 → 4012
Calls
4 calls:
117.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
24.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
21.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

series1.2s

Counts
4 → 12
Calls
4 calls:
774.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
137.0ms
(/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i)))
120.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))
148.0ms
(/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))

simplify1.8s

Algorithm
egg-herbie
Counts
4024 → 4024
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
05302195655

prune15.4s

Filtered
4024 candidates to 2893 candidates (71.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New402044024
Fresh224
Picked101
Done000
Total402364029

Merged error: 32.6b

Counts
4029 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
0.1b
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
0.5b
(/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))))
35.4b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
1388×times-frac
531×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
162×add-exp-log
151×associate-/r/
122×add-cbrt-cube
108×div-exp
97×div-inv
76×cbrt-undiv
61×associate-/r*
46×frac-times associate-*r/ associate-*l/
24×prod-exp
19×associate-/l*
16×cbrt-unprod
8×1-exp
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
1×associate-/l/
Counts
4 → 685
Calls
4 calls:
6.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
43.0ms
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
29.0ms
(/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

series2.8s

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
2.3s
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
255.0ms
(/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))))
131.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))

simplify293.0ms

Algorithm
egg-herbie
Counts
697 → 697
Iterations

Useful iterations: 1 (62.0ms)

IterNodesCost
0369926860
1500126009

prune2.8s

Filtered
697 candidates to 551 candidates (79.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New6943697
Fresh325
Picked011
Done000
Total6976703

Merged error: 2.7b

Counts
703 → 6

regimes136.0ms

Accuracy

44.6% (9.0b remaining)

Error of 10.9b against oracle of 1.9b and baseline of 18.2b

bsearch147.0ms

Steps
ItersRangePoint
4
2.0349362852184543e+135
2.7705215569966654e+135
2.701560437767458e+135
5
2.9130216729429826e+68
7.93051816434265e+68
2.9631628157961136e+68
8
3.1309119157309366e+59
3.968424382596194e+62
3.2601626280925855e+62

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05197
15197

end0.0ms

sample816.0ms

Algorithm
intervals
Results
447.0ms8000×body80valid
178.0ms8000×pre80true