Details

Time bar (total: 14.3s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×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: 51.8b

localize22.0ms

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)))
40.6b
(/ (* (* (- (* (+ (+ 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))))
42.2b
(/ (* 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)))))

rewrite414.0ms

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:
121.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
92.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
104.0ms
(/ (* (* (- (* (+ (+ 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))))
93.0ms
(/ (* 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)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
537.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
279.0ms
(* (- (* (+ (+ 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 i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
767.0ms
(/ (* 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)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
07943237
150022435

prune485.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 46.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
8.3b
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
36.5b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
41.9b
(* (/ (* 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))))))

rewrite538.0ms

Algorithm
rewrite-expression-head
Rules
256×*-un-lft-identity
247×times-frac
130×add-sqr-sqrt
121×add-cube-cbrt
81×distribute-lft-out
70×associate-*r*
66×add-exp-log
52×add-cbrt-cube
28×div-exp
21×cbrt-undiv
20×prod-exp
19×associate-/r*
16×div-inv
13×cbrt-unprod
9×associate-*l* associate-/l*
6×pow1 associate-/r/
4×expm1-log1p-u 1-exp log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+ unswap-sqr
2×associate-/l/
1×frac-times associate-*r/ pow-prod-down associate-*l/ *-commutative
Counts
4 → 274
Calls
4 calls:
38.0ms
(/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
136.0ms
(/ (* 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))))
346.0ms
(* (/ (* 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))))))

series1.5s

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
304.0ms
(/ (* i 1) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
102.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))
981.0ms
(* (/ (* 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))))))

simplify75.0ms

Algorithm
egg-herbie
Counts
286 → 286
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011065824
150024977

prune963.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 46.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
1.4b
(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
8.3b
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
40.9b
(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

rewrite442.0ms

Algorithm
rewrite-expression-head
Rules
276×times-frac
142×*-un-lft-identity
122×add-sqr-sqrt add-cube-cbrt
79×add-exp-log
49×add-cbrt-cube
47×div-exp
31×associate-/r/
28×div-inv
26×cbrt-undiv
22×associate-/r*
18×associate-/l*
16×flip3-+ flip-+
12×distribute-lft-out
10×prod-exp
6×cbrt-unprod
5×pow1 rec-exp 1-exp
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
1×pow-flip associate-*r/ inv-pow
Counts
4 → 277
Calls
4 calls:
36.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
2.0ms
(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
154.0ms
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
235.0ms
(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

series1.7s

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
133.0ms
(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
379.0ms
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
1.1s
(/ (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))

simplify106.0ms

Algorithm
egg-herbie
Counts
289 → 289
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014118290
150017393

prune933.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 46.2b

localize28.0ms

Local error

Found 4 expressions with local error:

34.5b
(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
34.5b
(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
36.0b
(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
36.0b
(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
44×sqrt-prod
32×add-sqr-sqrt
28×times-frac
24×*-un-lft-identity
22×add-cube-cbrt
10×pow1
8×rem-sqrt-square sqrt-pow1
4×add-exp-log expm1-log1p-u pow1/2 sqrt-div associate-/r/ add-cbrt-cube log1p-expm1-u div-inv add-log-exp
2×pow-flip flip3-+ flip-+ inv-pow
Counts
4 → 104
Calls
4 calls:
3.0ms
(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
3.0ms
(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
150.0ms
(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
154.0ms
(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))

series1.6s

Counts
4 → 12
Calls
4 calls:
85.0ms
(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
86.0ms
(sqrt (/ 1 (fma beta alpha (* i (+ (+ alpha beta) i)))))
715.0ms
(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
722.0ms
(sqrt (/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))

simplify47.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02661556
19611482
250011454

prune559.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 46.2b

regimes144.0ms

Accuracy

24.1% (3.2b remaining)

Error of 48.1b against oracle of 44.8b and baseline of 49.1b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02952
12952

end0.0ms

sample667.0ms

Algorithm
intervals
Results
353.0ms8000×body80valid
126.0ms8000×pre80true