Details

Time bar (total: 12.4s)

sample27.0ms

Algorithm
intervals
Results
12.0ms256×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: 50.9b

localize21.0ms

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)))
40.1b
(/ (* 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)))))
41.7b
(/ (* (* (- (* (+ (+ 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))))

rewrite408.0ms

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:
119.0ms
(* (* (- (* (+ (+ 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)))
90.0ms
(/ (* 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)))))
103.0ms
(/ (* (* (- (* (+ (+ 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))))

series3.3s

Counts
4 → 12
Calls
4 calls:
484.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
254.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
727.0ms
(/ (* 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))))

simplify47.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
07943237
150022435

prune445.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 45.8b

localize26.0ms

Local error

Found 4 expressions with local error:

8.0b
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
35.2b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.2b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
44.8b
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite504.0ms

Algorithm
rewrite-expression-head
Rules
211×times-frac
208×*-un-lft-identity
115×associate-*r*
113×add-sqr-sqrt
98×add-cube-cbrt
66×distribute-lft-out
52×sqrt-prod
45×add-exp-log add-cbrt-cube
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×associate-*l*
8×pow1 div-inv
5×associate-/r/
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×associate-/r*
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative associate-/l*
Counts
4 → 215
Calls
4 calls:
354.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
136.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.5s

Counts
4 → 12
Calls
4 calls:
967.0ms
(* (/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))) (/ (+ (+ alpha beta) i) (/ (fma i 2.0 (+ alpha beta)) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))))
56.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
57.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
460.0ms
(/ (* i (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify83.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
011075952
150025104

prune695.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 45.8b

localize25.0ms

Local error

Found 4 expressions with local error:

9.7b
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
27.5b
(* i (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
35.2b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
35.2b
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite420.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
38×times-frac
35×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
24×associate-*r*
11×add-exp-log add-cbrt-cube
8×pow1
6×associate-/l*
4×expm1-log1p-u associate-/r/ log1p-expm1-u add-log-exp
3×associate-*l* associate-/r* unswap-sqr
2×cbrt-undiv rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-exp prod-exp cbrt-unprod flip-+ div-inv
1×frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 119
Calls
4 calls:
137.0ms
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
277.0ms
(* i (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
576.0ms
(/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))
488.0ms
(* i (/ (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0)))))
55.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))
60.0ms
(sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify73.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04362244
119802035
250011996

prune660.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 45.8b

localize26.0ms

Local error

Found 4 expressions with local error:

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))))
47.5b
(/ (* i (* (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
11×add-cbrt-cube
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac pow1/3 div-exp prod-exp associate-/r* cbrt-unprod
2×associate-/r/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l*
Counts
4 → 66
Calls
4 calls:
0.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
0.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
1.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
145.0ms
(/ (* i (* (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

series1.3s

Counts
4 → 12
Calls
4 calls:
177.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
181.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
179.0ms
(cbrt (fma beta alpha (* i (+ (+ alpha beta) i))))
782.0ms
(/ (* i (* (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))) (cbrt (fma beta alpha (* i (+ (+ alpha beta) i)))))) (+ (pow (+ (+ alpha beta) (* 2.0 i)) 3) (* (fma i 2.0 (+ alpha beta)) (- 1.0))))

simplify67.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
04761267
121161059
250011013

prune378.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 45.8b

regimes224.0ms

Accuracy

31.3% (3.1b remaining)

Error of 47.0b against oracle of 43.9b and baseline of 48.4b

bsearch56.0ms

Steps
ItersRangePoint
7
2.2311381873559525e+79
8.2012024389677e+80
2.3218698039888783e+79

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03828
14228
24328
34328

end0.0ms

sample680.0ms

Algorithm
intervals
Results
380.0ms8000×body80valid
124.0ms8000×pre80true