Details

Time bar (total: 10.8s)

sample33.0ms

Algorithm
intervals
Results
13.0ms256×body80valid
6.0ms256×pre80true

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

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: 52.1b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
36.0b
(/ (* 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)))))
41.1b
(/ (* (* (- (* (+ (+ 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))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
49×add-exp-log add-cbrt-cube
21×add-sqr-sqrt
17×cbrt-undiv div-exp
16×add-cube-cbrt *-un-lft-identity times-frac
15×prod-exp cbrt-unprod
13×pow1
10×associate-/r*
8×associate-*l/
7×flip3-+ associate-*l* flip-+
6×associate-*r*
4×expm1-log1p-u frac-times associate-*r/ log1p-expm1-u div-inv associate-/l/ add-log-exp
3×swap-sqr
2×distribute-rgt-in flip3-- frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative flip-- fma-udef associate-/l* unswap-sqr
1×pow2 pow-plus associate-/r/ pow-sqr pow-prod-up difference-of-squares
Counts
4 → 135
Calls
4 calls:
13.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
16.0ms
(* (- (* (+ (+ 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)))))
22.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.0s

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))
267.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
750.0ms
(/ (* 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))))

simplify54.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09113106
150022350

prune458.0ms

Filtered
147 candidates to 105 candidates (71.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1389147
Fresh101
Picked101
Done000
Total1409149

Merged error: 32.9b

Counts
149 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
4.8b
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
27.0b
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
30.8b
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
77×times-frac
65×*-un-lft-identity
62×add-sqr-sqrt
61×add-exp-log add-cbrt-cube
50×add-cube-cbrt
29×cbrt-undiv div-exp
19×associate-*r* associate-/r*
13×associate-*l*
12×prod-exp cbrt-unprod
9×distribute-lft-out
7×div-inv associate-/l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg clear-num associate-/l/
2×frac-times associate-*r/ associate-*l/
1×pow-prod-down associate-/r/ *-commutative
Counts
4 → 179
Calls
4 calls:
20.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
15.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
3.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
3.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.4s

Counts
4 → 12
Calls
4 calls:
341.0ms
(* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta))))
749.0ms
(/ (* (/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0))) (/ (+ (+ alpha beta) i) (fma i 2.0 (+ alpha beta)))) (/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i)))))
166.0ms
(/ i (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)))
96.0ms
(/ (fma i 2.0 (+ alpha beta)) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify123.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
08383659
148932981
250012981

prune564.0ms

Filtered
191 candidates to 137 candidates (71.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1856191
Fresh628
Picked101
Done000
Total1928200

Merged error: 32.9b

Counts
200 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.6b
(/ 1 (* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
35.6b
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i)))
35.6b
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
171×add-exp-log
97×add-cbrt-cube
72×div-exp
62×prod-exp
38×cbrt-undiv
32×cbrt-unprod
18×add-sqr-sqrt
16×times-frac
14×add-cube-cbrt *-un-lft-identity
10×rec-exp 1-exp
9×pow1 associate-*l*
7×associate-*r* associate-/r/ associate-/l*
6×associate-*r/
5×associate-/r* div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×frac-times pow-flip flip3-+ pow-prod-down associate-*l/ flip-+ unswap-sqr
1×*-commutative inv-pow
Counts
4 → 163
Calls
4 calls:
15.0ms
(* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
17.0ms
(/ 1 (* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
9.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i)))
6.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.5s

Counts
4 → 12
Calls
4 calls:
411.0ms
(* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
762.0ms
(/ 1 (* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
172.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (* i (+ (+ alpha beta) i)))
143.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify118.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
08254165
141873129
250023119

prune382.0ms

Filtered
175 candidates to 95 candidates (54.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1741175
Fresh077
Picked011
Done000
Total1749183

Merged error: 29.0b

Counts
183 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.1b
(/ i (* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
34.0b
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))
35.6b
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
64×*-un-lft-identity
61×add-exp-log add-cbrt-cube
43×times-frac
39×add-sqr-sqrt
29×add-cube-cbrt
24×cbrt-undiv div-exp
21×associate-*l* distribute-lft-out
17×prod-exp cbrt-unprod
9×associate-/r*
7×associate-*r* associate-/r/ associate-/l*
6×pow1
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×frac-2neg clear-num
2×frac-times flip3-+ associate-*r/ associate-*l/ flip-+
1×pow-prod-down *-commutative
Counts
4 → 156
Calls
4 calls:
16.0ms
(* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
14.0ms
(/ i (* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
8.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))
5.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.4s

Counts
4 → 12
Calls
4 calls:
320.0ms
(* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
764.0ms
(/ i (* (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
152.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))
138.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify100.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07293632
135642899
250012892

prune406.0ms

Filtered
168 candidates to 110 candidates (65.5%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1662168
Fresh167
Picked101
Done011
Total1689177

Merged error: 29.0b

Counts
177 → 9

regimes153.0ms

Accuracy

66.7% (2.7b remaining)

Error of 34.3b against oracle of 31.6b and baseline of 39.7b

bsearch1.0ms

Steps
ItersRangePoint
0
1.2012081900001756e+153
1.2084065075766587e+153
1.204807348788417e+153

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03427
13427

end0.0ms

sample791.0ms

Algorithm
intervals
Results
432.0ms8000×body80valid
172.0ms8000×pre80true