Details

Time bar (total: 13.4s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.4b

localize23.0ms

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)))
37.2b
(/ (* 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)))))
40.4b
(/ (* (* (- (* (+ (+ 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))))

rewrite843.0ms

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:
258.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
187.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
169.0ms
(/ (* 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)))))
224.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.2s

Counts
4 → 12
Calls
4 calls:
463.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
240.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
738.0ms
(/ (* 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)))))
1.8s
(/ (* (* (- (* (+ (+ 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))))

simplify50.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
07943237
150022435

prune454.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 44.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
0.7b
(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
9.3b
(/ (* 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))))
36.5b
(/ (/ (* 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)))))

rewrite784.0ms

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:
67.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
5.0ms
(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
276.0ms
(/ (* 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))))
420.0ms
(/ (/ (* 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)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
115.0ms
(/ 1 (fma beta alpha (* i (+ (+ alpha beta) i))))
348.0ms
(/ (* 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))))
962.0ms
(/ (/ (* 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)))))

simplify98.0ms

Algorithm
egg-herbie
Counts
289 → 289
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014118290
150017393

prune928.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 44.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
0.0b
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
2.7b
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
44.7b
(/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
71×times-frac
51×add-sqr-sqrt
46×add-cube-cbrt
34×add-exp-log add-cbrt-cube
21×distribute-lft-out
19×associate-*r* associate-/r*
14×cbrt-undiv div-exp
9×associate-/l*
6×pow1 prod-exp cbrt-unprod div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*l* clear-num associate-/l/
2×associate-*r/ unswap-sqr
1×flip3-+ pow-prod-down associate-/r/ *-commutative flip-+
Counts
4 → 161
Calls
4 calls:
79.0ms
(* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
68.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
48.0ms
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
83.0ms
(* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
68.0ms
(/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))
861.0ms
(/ (* i (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
224.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify106.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06632752
136772392
250012392

prune565.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 37.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta)))))
0.1b
(* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta))))
2.7b
(/ (* i (* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta))))) (/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
44.7b
(/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite276.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log
52×add-cbrt-cube
51×times-frac
42×add-sqr-sqrt
41×*-un-lft-identity
35×add-cube-cbrt
31×prod-exp
27×div-exp
17×cbrt-undiv cbrt-unprod
16×associate-/r*
15×associate-*r/
14×associate-*r*
11×pow1
8×associate-*l*
6×frac-times flip3-+ associate-*l/ flip-+ associate-/l/
5×div-inv
4×expm1-log1p-u rec-exp 1-exp pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×un-div-inv distribute-lft-out unswap-sqr
2×frac-2neg clear-num *-commutative
1×associate-/r/
Counts
4 → 169
Calls
4 calls:
79.0ms
(* i (* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta)))))
87.0ms
(* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta))))
98.0ms
(/ (* i (* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta))))) (/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
83.0ms
(* i (* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta)))))
62.0ms
(* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta))))
860.0ms
(/ (* i (* (+ (+ alpha beta) i) (/ 1 (fma i 2.0 (+ alpha beta))))) (/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
221.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (- 1.0) (pow (fma i 2.0 (+ alpha beta)) 3)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify141.0ms

Algorithm
egg-herbie
Counts
181 → 181
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08243098
148432576
250012576

prune575.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 37.6b

regimes145.0ms

Accuracy

73.1% (2.8b remaining)

Error of 41.6b against oracle of 38.8b and baseline of 49.1b

bsearch54.0ms

Steps
ItersRangePoint
7
3.3465513178816536e+100
6.48140642308104e+101
6.388557784475249e+101

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03631
13631

end0.0ms

sample872.0ms

Algorithm
intervals
Results
354.0ms8000×body80valid
267.0ms8000×pre80true