Details

Time bar (total: 22.0s)

sample28.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

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: 51.9b

Counts
2 → 2

localize22.0ms

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)))
39.6b
(/ (* 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)))))
41.5b
(/ (* (* (- (* (+ (+ 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))))

rewrite439.0ms

Algorithm
rewrite-expression-head
Rules
3026×times-frac
2577×associate-*l*
2573×*-un-lft-identity
2204×add-sqr-sqrt
1117×add-cube-cbrt
829×associate-*r*
624×distribute-lft-out
361×unswap-sqr
312×distribute-lft-out--
260×difference-of-squares
259×*-commutative
109×associate-/r*
80×associate-/l*
52×add-exp-log swap-sqr add-cbrt-cube
41×associate-/r/
17×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
14×associate-*l/
11×pow1
6×associate-/l/
4×expm1-log1p-u flip3-- pow-prod-down flip-- fma-udef log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×distribute-rgt-in distribute-lft-in associate-*r/
1×flip3-+ flip-+
Counts
4 → 1868
Calls
4 calls:
49.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
38.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
104.0ms
(/ (* 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)))))
51.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.9s

Counts
4 → 12
Calls
4 calls:
566.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
497.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
803.0ms
(/ (* 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))))

simplify631.0ms

Algorithm
egg-herbie
Counts
1880 → 1880
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
0500166450

prune4.1s

Filtered
1880 candidates to 878 candidates (46.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New187461880
Fresh101
Picked101
Done000
Total187661882

Merged error: 36.7b

Counts
1882 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ alpha beta) i) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
5.0b
(* (/ i (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) (/ (+ (+ alpha beta) i) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
30.3b
(/ i (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
40.5b
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite554.0ms

Algorithm
rewrite-expression-head
Rules
3134×*-un-lft-identity
2253×add-sqr-sqrt
2088×times-frac
1941×associate-/r*
1322×add-cube-cbrt
1180×frac-times
823×associate-*l*
765×distribute-lft-out
576×associate-*r*
402×distribute-lft-out--
375×swap-sqr
341×associate-/l*
335×difference-of-squares
185×unswap-sqr
172×*-commutative
87×clear-num
86×frac-2neg
59×associate-*r/
52×add-exp-log add-cbrt-cube
46×associate-/r/
44×associate-/l/
37×div-inv
22×cbrt-undiv flip3-+ div-exp flip-+
20×associate-*l/
12×prod-exp cbrt-unprod
6×pow1
4×expm1-log1p-u un-div-inv log1p-expm1-u add-log-exp
2×flip3-- flip--
1×pow-prod-down
Counts
4 → 2116
Calls
4 calls:
23.0ms
(/ (+ (+ alpha beta) i) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
255.0ms
(* (/ i (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) (/ (+ (+ alpha beta) i) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
34.0ms
(/ i (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
8.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.3s

Counts
4 → 12
Calls
4 calls:
153.0ms
(/ (+ (+ alpha beta) i) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
776.0ms
(* (/ i (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) (/ (+ (+ alpha beta) i) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))))
186.0ms
(/ i (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
156.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify622.0ms

Algorithm
egg-herbie
Counts
2128 → 2128
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0500161859

prune3.1s

Filtered
2128 candidates to 781 candidates (36.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New211992128
Fresh505
Picked101
Done000
Total212592134

Merged error: 34.2b

Counts
2134 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (fma i 2.0 (+ alpha beta)))
0.6b
(cbrt (fma i 2.0 (+ alpha beta)))
0.6b
(cbrt (fma i 2.0 (+ alpha beta)))
37.6b
(/ (* (cbrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
48×times-frac
40×add-cube-cbrt *-un-lft-identity
25×cbrt-prod
24×associate-*l*
16×associate-/l*
12×associate-*r*
11×add-cbrt-cube
9×add-exp-log
8×unswap-sqr
4×pow1 expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
3×cbrt-undiv pow1/3 associate-/r*
2×div-exp cbrt-unprod
1×frac-2neg prod-exp clear-num div-inv
Counts
4 → 123
Calls
4 calls:
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
8.0ms
(/ (* (cbrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
259.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
259.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
258.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
467.0ms
(/ (* (cbrt (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify60.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04351859
117421763
250031730

prune772.0ms

Filtered
135 candidates to 115 candidates (85.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1314135
Fresh178
Picked101
Done000
Total13311144

Merged error: 34.0b

Counts
144 → 11

localize31.0ms

Local error

Found 4 expressions with local error:

18.5b
(/ (* (cbrt (fma i 2.0 (+ alpha beta))) (sqrt (fma i 2.0 (+ alpha beta)))) (* (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))))
36.1b
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.1b
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
36.1b
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
745×add-sqr-sqrt
567×times-frac
501×cbrt-prod
345×add-cube-cbrt *-un-lft-identity
300×associate-*r* associate-*l*
200×unswap-sqr
140×sqrt-prod
132×swap-sqr
50×*-commutative
39×add-cbrt-cube
27×associate-/r*
22×cbrt-unprod
21×associate-/l*
16×add-exp-log
15×cbrt-undiv
4×pow1 expm1-log1p-u div-exp prod-exp log1p-expm1-u add-log-exp
3×pow1/3
1×frac-2neg clear-num div-inv
Counts
4 → 685
Calls
4 calls:
29.0ms
(/ (* (cbrt (fma i 2.0 (+ alpha beta))) (sqrt (fma i 2.0 (+ alpha beta)))) (* (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
630.0ms
(/ (* (cbrt (fma i 2.0 (+ alpha beta))) (sqrt (fma i 2.0 (+ alpha beta)))) (* (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))))
185.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
183.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
184.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify241.0ms

Algorithm
egg-herbie
Counts
697 → 697
Iterations

Useful iterations: 1 (49.0ms)

IterNodesCost
0227321810
1500121244

prune2.5s

Filtered
697 candidates to 389 candidates (55.8%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New6943697
Fresh3710
Picked101
Done000
Total69810708

Merged error: 34.0b

Counts
708 → 10

regimes239.0ms

Accuracy

33% (3.0b remaining)

Error of 37.2b against oracle of 34.2b and baseline of 38.7b

bsearch94.0ms

Steps
ItersRangePoint
9
1.814346932338433e+210
1.3703176336150656e+219
1.8523098755484387e+210

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05880
15880

end0.0ms

sample669.0ms

Algorithm
intervals
Results
354.0ms8000×body80valid
131.0ms8000×pre80true