Details

Time bar (total: 15.3s)

sample32.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
5.0ms256×pre80true

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

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: 51.5b

Counts
2 → 2

localize20.0ms

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)))
40.9b
(/ (* 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)))))
41.5b
(/ (* (* (- (* (+ (+ 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))))

rewrite79.0ms

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:
17.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
17.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
21.0ms
(/ (* 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))))

series3.4s

Counts
4 → 12
Calls
4 calls:
512.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
268.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (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 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 (24.0ms)

IterNodesCost
07943237
150022435

prune441.0ms

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: 45.5b

Counts
136 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

7.6b
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
36.4b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.4b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
45.2b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
211×times-frac
208×*-un-lft-identity
115×associate-*r*
113×add-sqr-sqrt
98×add-cube-cbrt
66×distribute-lft-out
52×sqrt-prod
45×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-*l*
8×pow1 div-inv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 215
Calls
4 calls:
55.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
20.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
59.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
487.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify80.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
011075954
150015104

prune647.0ms

Filtered
227 candidates to 126 candidates (55.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2261227
Fresh077
Picked011
Done000
Total2269235

Merged error: 45.5b

Counts
235 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

5.6b
(/ (/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
6.3b
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
32.3b
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
36.6b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
3226×times-frac
2239×*-un-lft-identity
1259×add-sqr-sqrt add-cube-cbrt
588×distribute-lft-out
165×div-inv
81×associate-/l*
34×add-exp-log add-cbrt-cube
32×associate-/r*
20×cbrt-undiv div-exp
16×associate-/r/
5×associate-/l/
4×pow1 expm1-log1p-u frac-2neg clear-num log1p-expm1-u add-log-exp
2×flip3-+ div-sub distribute-rgt-neg-out flip-+
1×unsub-neg
Counts
4 → 1183
Calls
4 calls:
47.0ms
(/ (/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
19.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
19.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
3.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
420.0ms
(/ (/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
526.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
491.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
101.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify486.0ms

Algorithm
egg-herbie
Counts
1195 → 1195
Iterations

Useful iterations: 1 (79.0ms)

IterNodesCost
0439647810
1500147621

prune3.5s

Filtered
1195 candidates to 680 candidates (56.9%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New119411195
Fresh257
Picked011
Done011
Total119681204

Merged error: 39.9b

Counts
1204 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.2b
(* 12.0 (* i beta))
36.3b
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
36.6b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
661×times-frac
519×*-un-lft-identity
289×add-sqr-sqrt add-cube-cbrt
138×distribute-lft-out
37×div-inv
27×associate-/l*
25×add-exp-log add-cbrt-cube
19×associate-/r*
10×cbrt-undiv div-exp
9×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* pow-prod-down prod-exp clear-num cbrt-unprod associate-/l/
1×flip3-+ associate-*r* associate-/r/ *-commutative flip-+
Counts
4 → 389
Calls
4 calls:
22.0ms
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.0ms
(* 12.0 (* i beta))
8.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
3.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
227.0ms
(/ (/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta))))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
19.0ms
(* 12.0 (* i beta))
98.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))
98.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify139.0ms

Algorithm
egg-herbie
Counts
401 → 401
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0144911450
1500111123

prune1.2s

Filtered
401 candidates to 248 candidates (61.8%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3992401
Fresh145
Picked101
Done022
Total4018409

Merged error: 12.6b

Counts
409 → 8

regimes171.0ms

Accuracy

56.4% (2.9b remaining)

Error of 14.8b against oracle of 11.9b and baseline of 18.6b

bsearch26.0ms

Steps
ItersRangePoint
3
5.040828044076301e+97
5.981957486714115e+97
5.452572175230344e+97

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03421
13821
23921
33921

end0.0ms

sample783.0ms

Algorithm
intervals
Results
422.0ms8000×body80valid
170.0ms8000×pre80true