Details

Time bar (total: 15.3s)

sample40.0ms

Algorithm
intervals
Results
21.0ms256×body80valid
6.0ms256×pre80true

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
37.7b
(/ (* 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)))))
39.4b
(/ (* (* (- (* (+ (+ 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))))

rewrite387.0ms

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:
113.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
86.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
85.0ms
(/ (* 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)))))
99.0ms
(/ (* (* (- (* (+ (+ 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:
542.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
280.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
786.0ms
(/ (* 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)))))
2.0s
(/ (* (* (- (* (+ (+ 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))))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435

prune482.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 42.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))
7.8b
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
33.3b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
37.5b
(* (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))

rewrite581.0ms

Algorithm
rewrite-expression-head
Rules
133×*-un-lft-identity
128×times-frac
77×add-sqr-sqrt
70×associate-*r*
68×add-cube-cbrt
61×add-exp-log
47×add-cbrt-cube
39×distribute-lft-out
25×div-exp
20×prod-exp
18×cbrt-undiv
13×cbrt-unprod
12×fma-def
9×associate-*l* div-inv
6×pow1 associate-/r* add-log-exp
5×associate-/r/
4×expm1-log1p-u 1-exp log1p-expm1-u associate-/l*
3×unpow-prod-down flip3-+ cube-prod flip-+ unswap-sqr
2×frac-2neg clear-num distribute-rgt-neg-out
1×+-commutative cube-mult frac-times unpow3 associate-*r/ unsub-neg pow-prod-down associate-*l/ sum-log *-commutative sqr-pow
Counts
4 → 199
Calls
4 calls:
121.0ms
(+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))
127.0ms
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
321.0ms
(* (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))

series1.8s

Counts
4 → 12
Calls
4 calls:
400.0ms
(+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))
295.0ms
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
100.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
987.0ms
(* (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
211 → 211
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09734073
150013277

prune718.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 42.7b

localize27.0ms

Local error

Found 4 expressions with local error:

33.1b
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
33.1b
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
33.3b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
33.3b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
248×*-un-lft-identity
244×times-frac
140×sqrt-prod
130×add-sqr-sqrt
118×add-cube-cbrt
78×distribute-lft-out
14×div-inv
8×add-exp-log add-cbrt-cube
6×pow1 rem-sqrt-square associate-/r* associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-exp clear-num associate-/r/
Counts
4 → 228
Calls
4 calls:
27.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
25.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
2.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series475.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
144.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
105.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
101.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify71.0ms

Algorithm
egg-herbie
Counts
240 → 240
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
04384456
113794256
250014040

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 42.7b

localize34.0ms

Local error

Found 4 expressions with local error:

31.9b
(sqrt (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
33.1b
(sqrt (/ (+ (+ alpha beta) i) (/ (sqrt (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (sqrt (fma i 2.0 (+ alpha beta)))))))
33.1b
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
33.3b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite382.0ms

Algorithm
rewrite-expression-head
Rules
2027×times-frac
1566×*-un-lft-identity
1374×sqrt-prod
848×add-sqr-sqrt
816×add-cube-cbrt
450×distribute-lft-out
44×div-inv
12×rem-sqrt-square
9×associate-/r/
7×pow1
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-pow1 pow1/2 sqrt-div associate-/r* associate-/l*
1×cbrt-undiv frac-2neg flip3-+ div-exp clear-num flip-+
Counts
4 → 846
Calls
4 calls:
131.0ms
(sqrt (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
110.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (sqrt (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (sqrt (fma i 2.0 (+ alpha beta)))))))
26.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
7.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.1s

Counts
4 → 12
Calls
4 calls:
577.0ms
(sqrt (/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
128.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (sqrt (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (sqrt (fma i 2.0 (+ alpha beta)))))))
124.0ms
(sqrt (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))))
245.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify282.0ms

Algorithm
egg-herbie
Counts
858 → 858
Iterations

Useful iterations: 1 (46.0ms)

IterNodesCost
0263428393
1500127278

prune2.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 42.7b

regimes233.0ms

Accuracy

38.4% (2.6b remaining)

Error of 47.2b against oracle of 44.6b and baseline of 48.9b

bsearch57.0ms

Steps
ItersRangePoint
7
2.8404774197940265e+96
1.1761752444596657e+98
4.144911625120832e+96

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03922
15122
25222
35222

end0.0ms

sample1.1s

Algorithm
intervals
Results
697.0ms8000×body80valid
179.0ms8000×pre80true