Details

Time bar (total: 12.8s)

sample31.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
5.0ms256×pre80true

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune12.0ms

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: 52.1b

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)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
40.1b
(/ (* (* (- (* (+ (+ 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))))
41.0b
(/ (* 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)))))

rewrite73.0ms

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)))
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))) (fma beta alpha (* i (+ (+ alpha beta) i))))
19.0ms
(/ (* 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)))))

series3.3s

Counts
4 → 12
Calls
4 calls:
504.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
258.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
1.8s
(/ (* (* (- (* (+ (+ 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))))
734.0ms
(/ (* 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)))))

simplify50.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435

prune410.0ms

Filtered
134 candidates to 97 candidates (72.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1286134
Fresh011
Picked101
Done000
Total1297136

Merged error: 47.4b

Counts
136 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

4.3b
(/ (/ (+ (+ 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)))))
7.2b
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
34.6b
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
34.7b
(/ (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:
43.0ms
(/ (/ (+ (+ 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)))))
17.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
18.0ms
(/ (+ (+ 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))))

series1.7s

Counts
4 → 12
Calls
4 calls:
573.0ms
(/ (/ (+ (+ 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)))))
529.0ms
(/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i)
480.0ms
(/ (+ (+ alpha beta) i) (/ (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))) i))
162.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify494.0ms

Algorithm
egg-herbie
Counts
1195 → 1195
Iterations

Useful iterations: 1 (79.0ms)

IterNodesCost
0439047810
1500147622

prune3.5s

Filtered
1195 candidates to 680 candidates (56.9%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New119231195
Fresh336
Picked101
Done000
Total119661202

Merged error: 41.6b

Counts
1202 → 6

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)))))
0.3b
(* 12.0 (* i beta))
34.7b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
34.9b
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))

rewrite61.0ms

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:
16.0ms
(/ (/ (+ (+ 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))
3.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
8.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (/ (+ (+ 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)))))
20.0ms
(* 12.0 (* i beta))
101.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
105.0ms
(/ (+ (+ alpha beta) i) (fma 8.0 (pow i 2) (fma 12.0 (* alpha i) (* 12.0 (* i beta)))))

simplify143.0ms

Algorithm
egg-herbie
Counts
401 → 401
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
0144911450
1500111125

prune1.2s

Filtered
401 candidates to 248 candidates (61.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3992401
Fresh145
Picked101
Done000
Total4016407

Merged error: 13.4b

Counts
407 → 6

localize0.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
000

prune0.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New000
Fresh055
Picked011
Done000
Total066

Merged error: 13.4b

Counts
6 → 6

regimes129.0ms

Accuracy

53.8% (3.1b remaining)

Error of 15.0b against oracle of 11.9b and baseline of 18.5b

bsearch51.0ms

Steps
ItersRangePoint
7
1.585736602217596e+74
8.085023751865787e+75
4.026004052733782e+75

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03828
14228
24328
34328

end0.0ms

sample809.0ms

Algorithm
intervals
Results
440.0ms8000×body80valid
174.0ms8000×pre80true