Details

Time bar (total: 21.1s)

sample28.0ms

Algorithm
intervals
Results
10.0ms256×body80valid
3.0ms256×pre80true

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 49.8b

localize20.0ms

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)))
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)))
39.3b
(/ (* (* (- (* (+ (+ 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))))
40.1b
(/ (* 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)))))

rewrite867.0ms

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:
194.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
267.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
225.0ms
(/ (* (* (- (* (+ (+ 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))))
178.0ms
(/ (* 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)))))

series3.2s

Counts
4 → 12
Calls
4 calls:
238.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
452.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
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))))
701.0ms
(/ (* 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

prune456.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 44.5b

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b
(exp (log (/ (* 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)))))))
4.4b
(log (/ (* 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))))))
39.3b
(/ (* (* (- (* (+ (+ 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))))
40.1b
(/ (* 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)))))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
78×add-exp-log
45×add-cbrt-cube
36×times-frac
31×div-exp
24×log-prod
23×prod-exp
17×cbrt-undiv add-sqr-sqrt add-cube-cbrt *-un-lft-identity
13×cbrt-unprod
12×exp-sum
10×associate-/r*
9×rem-log-exp
8×div-inv
6×pow1
4×expm1-log1p-u exp-prod associate-*l/ log1p-expm1-u associate-/l/ add-log-exp
3×associate-/r/
2×log-div frac-2neg associate-*r/ clear-num log-pow associate-/l*
1×flip3-- flip3-+ exp-diff flip-- flip-+ rem-exp-log
Counts
4 → 132
Calls
4 calls:
608.0ms
(exp (log (/ (* 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)))))))
155.0ms
(log (/ (* 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))))))
228.0ms
(/ (* (* (- (* (+ (+ 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))))
176.0ms
(/ (* 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)))))

series12.1s

Counts
4 → 12
Calls
4 calls:
724.0ms
(exp (log (/ (* 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)))))))
8.9s
(log (/ (* 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))))
732.0ms
(/ (* 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)))))

simplify126.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07213992
144813183
250013176

prune506.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 9.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.25 (/ 1 (pow i 2)) (log 0.0625))
0.0b
(exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))
1.2b
(/ 1 (pow i 2))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
21×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×add-exp-log unpow-prod-down
8×associate-/r*
6×div-exp
5×add-cbrt-cube
4×unpow2 add-log-exp sqr-pow
3×pow1 expm1-log1p-u pow-to-exp rec-exp exp-prod 1-exp pow-exp log1p-expm1-u associate-/l*
2×fma-udef
1×cbrt-undiv pow-flip frac-2neg exp-sum clear-num div-inv rem-exp-log inv-pow
Counts
3 → 83
Calls
3 calls:
0.0ms
(fma 0.25 (/ 1 (pow i 2)) (log 0.0625))
2.0ms
(exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))
9.0ms
(/ 1 (pow i 2))

series379.0ms

Counts
3 → 9
Calls
3 calls:
297.0ms
(fma 0.25 (/ 1 (pow i 2)) (log 0.0625))
63.0ms
(exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))
19.0ms
(/ 1 (pow i 2))

simplify151.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0217448
1797385
24296339
35001339

prune179.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.25 (/ 1 (pow i 2)) (log 0.0625))
0.0b
(exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))
1.2b
(/ 1 (pow i 2))
4.0b
(log (exp (exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log
12×unpow-prod-down
8×associate-/r*
7×exp-prod
6×div-exp add-cbrt-cube
5×pow1 log-pow add-log-exp
4×expm1-log1p-u log1p-expm1-u unpow2 sqr-pow
3×pow-to-exp rec-exp log-prod 1-exp pow-exp fma-udef associate-/l*
2×exp-sum
1×cbrt-undiv pow-flip frac-2neg rem-log-exp clear-num div-inv rem-exp-log inv-pow
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma 0.25 (/ 1 (pow i 2)) (log 0.0625))
2.0ms
(exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))
9.0ms
(/ 1 (pow i 2))
5.0ms
(log (exp (exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))))

series446.0ms

Counts
4 → 12
Calls
4 calls:
295.0ms
(fma 0.25 (/ 1 (pow i 2)) (log 0.0625))
69.0ms
(exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))
15.0ms
(/ 1 (pow i 2))
67.0ms
(log (exp (exp (fma 0.25 (/ 1 (pow i 2)) (log 0.0625)))))

simplify155.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0244608
1835527
24360481
35001481

prune209.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.1b

regimes194.0ms

Accuracy

44.4% (4.4b remaining)

Error of 14.6b against oracle of 10.2b and baseline of 18.2b

bsearch37.0ms

Steps
ItersRangePoint
5
1.4838874823865026e+135
3.093306085654252e+135
1.5075819044026248e+135

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04434
14434

end0.0ms

sample681.0ms

Algorithm
intervals
Results
341.0ms8000×body80valid
108.0ms8000×pre80true