Details

Time bar (total: 8.0s)

sample46.0ms

Algorithm
intervals
Results
24.0ms256×body80valid

simplify115.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
013286
161875
2334339
3500139

prune32.0ms

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: 29.8b

Counts
2 → 2

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x x) (* 2.0 0.0001789971))
0.2b
(* (* x x) 0.0001789971)
14.6b
(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
25.8b
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
62×add-sqr-sqrt
61×add-cube-cbrt *-un-lft-identity
31×associate-/r/
30×flip3-+ flip-+
28×add-exp-log add-cbrt-cube
24×associate-*r/ frac-add
22×associate-/r*
21×pow1
11×pow-prod-down prod-exp cbrt-unprod
6×div-inv associate-/l/ associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp associate-*r* log1p-expm1-u add-log-exp
2×frac-2neg associate-*l* clear-num *-commutative
1×unswap-sqr
Counts
4 → 182
Calls
4 calls:
7.0ms
(* (* x x) (* 2.0 0.0001789971))
6.0ms
(* (* x x) 0.0001789971)
21.0ms
(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
29.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

series543.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* x x) (* 2.0 0.0001789971))
23.0ms
(* (* x x) 0.0001789971)
273.0ms
(/ x (/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
217.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))

simplify119.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012069406
150028888

prune1.8s

Filtered
194 candidates to 158 candidates (81.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1904194
Fresh101
Picked101
Done000
Total1924196

Merged error: 0b

Counts
196 → 4

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* x x) 3)
0.2b
(pow (* x x) 4)
14.6b
(/ x (* 1 (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
25.8b
(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log
20×pow1
18×add-cbrt-cube
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
12×pow-pow times-frac
8×div-exp
6×pow-unpow prod-exp associate-/l*
5×cbrt-undiv
4×expm1-log1p-u pow-exp associate-/r* log1p-expm1-u add-log-exp
3×cbrt-unprod
2×pow2 pow-to-exp unpow-prod-down frac-2neg pow-plus 1-exp pow-prod-down clear-num pow-sqr pow-prod-up div-inv rem-cube-cbrt sqr-pow
1×cube-mult unpow3 cube-prod associate-*r/ associate-/r/
Counts
4 → 108
Calls
4 calls:
4.0ms
(pow (* x x) 3)
4.0ms
(pow (* x x) 4)
6.0ms
(/ x (* 1 (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
3.0ms
(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

series584.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(pow (* x x) 3)
46.0ms
(pow (* x x) 4)
278.0ms
(/ x (* 1 (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
218.0ms
(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04982634
121632224
250012188

prune853.0ms

Filtered
120 candidates to 81 candidates (67.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1182120
Fresh213
Picked101
Done000
Total1213124

Merged error: 0b

Counts
124 → 3

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (* (* x x) 2.0) 0.0001789971 0.0008327945)
0.2b
(pow (* x x) 4)
14.6b
(/ x (* 1 (/ (fma (fma x (* x 0.0140005442) 0.0694555761) (pow x 6) (fma (* (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) x) (pow (pow x 3) 3) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
25.8b
(/ (fma (fma x (* x 0.0140005442) 0.0694555761) (pow x 6) (fma (* (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) x) (pow (pow x 3) 3) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
15×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×pow1 times-frac
8×div-exp
6×pow-pow associate-/l*
5×cbrt-undiv prod-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×pow-unpow
2×frac-2neg 1-exp pow-exp clear-num cbrt-unprod div-inv
1×pow2 pow-to-exp unpow-prod-down pow-plus associate-*r/ pow-prod-down associate-/r/ pow-sqr pow-prod-up fma-udef sqr-pow
Counts
4 → 90
Calls
4 calls:
1.0ms
(fma (* (* x x) 2.0) 0.0001789971 0.0008327945)
4.0ms
(pow (* x x) 4)
6.0ms
(/ x (* 1 (/ (fma (fma x (* x 0.0140005442) 0.0694555761) (pow x 6) (fma (* (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) x) (pow (pow x 3) 3) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
3.0ms
(/ (fma (fma x (* x 0.0140005442) 0.0694555761) (pow x 6) (fma (* (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) x) (pow (pow x 3) 3) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

series625.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma (* (* x x) 2.0) 0.0001789971 0.0008327945)
47.0ms
(pow (* x x) 4)
290.0ms
(/ x (* 1 (/ (fma (fma x (* x 0.0140005442) 0.0694555761) (pow x 6) (fma (* (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) x) (pow (pow x 3) 3) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))
225.0ms
(/ (fma (fma x (* x 0.0140005442) 0.0694555761) (pow x 6) (fma (* (fma (* (* x x) 2.0) 0.0001789971 0.0008327945) x) (pow (pow x 3) 3) (fma 0.2909738639 (pow x 4) (fma (* 0.7715471019 x) x 1.0)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

simplify74.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04682401
119452029
250012012

prune709.0ms

Filtered
102 candidates to 70 candidates (68.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1020102
Fresh022
Picked011
Done000
Total1023105

Merged error: 0b

Counts
105 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma x 1.0 (- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3))))
0.0b
(* 0.265709700396151 (pow x 5))
0.1b
(* 0.6665536072 (pow x 3))
21.0b
(- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp add-log-exp
4×pow1 expm1-log1p-u cube-prod log1p-expm1-u sqr-pow
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×cube-mult sub-neg flip3-- fma-neg diff-log unpow3 prod-diff flip-- fma-udef
Counts
4 → 86
Calls
4 calls:
1.0ms
(fma x 1.0 (- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3))))
5.0ms
(* 0.265709700396151 (pow x 5))
6.0ms
(* 0.6665536072 (pow x 3))
4.0ms
(- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3)))

series287.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma x 1.0 (- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3))))
53.0ms
(* 0.265709700396151 (pow x 5))
34.0ms
(* 0.6665536072 (pow x 3))
141.0ms
(- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3)))

simplify55.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0297467
11264425
25001423

prune192.0ms

Filtered
98 candidates to 67 candidates (68.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New98098
Fresh011
Picked011
Done011
Total983101

Merged error: 0b

Counts
101 → 3

regimes41.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.3b

bsearch649.0ms

Steps
ItersRangePoint
10
0.475758948552502
3048118974.682059
1252.7892861378523
11
-9.198699199216347e+28
-71914824.75180596
-3.5491276599066634e+21

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07336
17536
27536

end0.0ms

sample885.0ms

Algorithm
intervals
Results
770.0ms8000×body80valid