Details

Time bar (total: 25.4s)

sample101.0ms

Algorithm
intervals
Results
60.0ms256×body80valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
33489
2608
1132
044

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.6b

localize115.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (* x x) 0.0001789971 0.0005064034)
0.4b
(* 0.0008327945 (* x x))
14.5b
(* (/ (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)
30.8b
(/ (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
19×times-frac
16×add-cbrt-cube associate-*l* add-exp-log
11×pow1
5×prod-exp cbrt-unprod
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u add-log-exp
3×associate-/r* associate-/l* unswap-sqr
2×cbrt-undiv div-exp *-commutative div-inv associate-/l/
1×clear-num frac-2neg flip3-+ associate-*l/ flip-+ fma-udef
Counts
4 → 96
Calls
4 calls:
0.0ms
(fma (* x x) 0.0001789971 0.0005064034)
12.0ms
(* 0.0008327945 (* x x))
39.0ms
(* (/ (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)
20.0ms
(/ (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))

series753.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(fma (* x x) 0.0001789971 0.0005064034)
31.0ms
(* 0.0008327945 (* x x))
340.0ms
(* (/ (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)
282.0ms
(/ (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))

simplify1.7s

Counts
108 → 108
Iterations
IterNodes
done5002
22713
1504
0203

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (/ 0.5 x) (/ 0.2514179000665375 (pow x 3))) (/ 0.15298196345929327 (pow x 5)))
0.1b
(/ 0.2514179000665375 (pow x 3))
0.5b
(/ 0.15298196345929327 (pow x 5))

rewrite361.0ms

Algorithm
rewrite-expression-head
Rules
62×*-un-lft-identity times-frac
45×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
13×add-exp-log
12×cube-prod
8×add-log-exp sqr-pow
7×add-cbrt-cube distribute-lft-out
6×div-exp associate-/l*
5×fma-def
4×cube-mult unpow3 frac-add
3×expm1-log1p-u pow1 sum-log log1p-expm1-u
2×pow-to-exp cbrt-undiv clear-num frac-2neg flip3-+ pow-exp flip-+ div-inv
1×+-commutative associate-+l+
Counts
3 → 140
Calls
3 calls:
333.0ms
(+ (+ (/ 0.5 x) (/ 0.2514179000665375 (pow x 3))) (/ 0.15298196345929327 (pow x 5)))
13.0ms
(/ 0.2514179000665375 (pow x 3))
11.0ms
(/ 0.15298196345929327 (pow x 5))

series231.0ms

Counts
3 → 9
Calls
3 calls:
69.0ms
(+ (+ (/ 0.5 x) (/ 0.2514179000665375 (pow x 3))) (/ 0.15298196345929327 (pow x 5)))
76.0ms
(/ 0.2514179000665375 (pow x 3))
85.0ms
(/ 0.15298196345929327 (pow x 5))

simplify1.3s

Counts
149 → 149
Iterations
IterNodes
done5000
22361
1537
0235

prune750.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize307.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))))
4.9b
(sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0)))))
26.3b
(/ (sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0))))) (sqrt (fma 2.0 (* 0.0001789971 (pow (pow x 2) 6)) (fma (pow (pow x 2) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (pow x 2) 0.7715471019 1.0)))))))
26.3b
(/ (sqrt (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0))))) (sqrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
90×sqrt-prod
72×times-frac
64×add-sqr-sqrt
62×*-un-lft-identity add-cube-cbrt
12×associate-/r* associate-/l*
8×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
2×cbrt-undiv rem-sqrt-square sqrt-undiv clear-num frac-2neg sqrt-pow1 flip3-+ pow1/2 div-exp flip-+ div-inv associate-/l/
Counts
4 → 160
Calls
4 calls:
19.0ms
(sqrt (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))))
1.0ms
(sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0)))))
6.0ms
(/ (sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0))))) (sqrt (fma 2.0 (* 0.0001789971 (pow (pow x 2) 6)) (fma (pow (pow x 2) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (pow x 2) 0.7715471019 1.0)))))))
17.0ms
(/ (sqrt (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0))))) (sqrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
224.0ms
(sqrt (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))))
221.0ms
(sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0)))))
416.0ms
(/ (sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0))))) (sqrt (fma 2.0 (* 0.0001789971 (pow (pow x 2) 6)) (fma (pow (pow x 2) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (pow x 2) 0.7715471019 1.0)))))))
403.0ms
(/ (sqrt (+ (* (pow (* x x) 4) (fma (* x x) 0.0001789971 0.0005064034)) (fma 0.0072644182 (pow x 6) (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (* x x) 1.0))))) (sqrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* 0.0008327945 (* x x))) (fma (pow x 6) 0.0694555761 (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))

simplify1.1s

Counts
172 → 172
Iterations
IterNodes
done5000
22264
1621
0305

prune3.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize273.0ms

Local error

Found 4 expressions with local error:

4.9b
(sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0)))))
14.4b
(sqrt (/ (fma (pow (* x x) 4) (fma x (* x 0.0001789971) 0.0005064034) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* x x) 0.1049934947 1.0)))) (fma 2.0 (* 0.0001789971 (pow (* x x) 6)) (fma (fma 0.0008327945 (* x x) 0.0140005442) (pow (* x x) 4) (fma (pow x 6) 0.0694555761 (fma (pow x 4) 0.2909738639 (fma x (* x 0.7715471019) 1.0)))))))
26.3b
(/ (sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0))))) (sqrt (fma 2.0 (* 0.0001789971 (pow (pow x 2) 6)) (fma (pow (pow x 2) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (pow x 2) 0.7715471019 1.0)))))))
30.8b
(/ (fma (pow (* x x) 4) (fma x (* x 0.0001789971) 0.0005064034) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* x x) 0.1049934947 1.0)))) (fma 2.0 (* 0.0001789971 (pow (* x x) 6)) (fma (fma 0.0008327945 (* x x) 0.0140005442) (pow (* x x) 4) (fma (pow x 6) 0.0694555761 (fma (pow x 4) 0.2909738639 (fma x (* x 0.7715471019) 1.0))))))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
58×sqrt-prod
55×times-frac
52×add-sqr-sqrt
48×*-un-lft-identity add-cube-cbrt
9×associate-/r* associate-/l*
8×add-cbrt-cube add-exp-log
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square div-inv
2×cbrt-undiv clear-num frac-2neg sqrt-pow1 pow1/2 div-exp
1×sqrt-undiv sqrt-div
Counts
4 → 134
Calls
4 calls:
2.0ms
(sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0)))))
6.0ms
(sqrt (/ (fma (pow (* x x) 4) (fma x (* x 0.0001789971) 0.0005064034) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* x x) 0.1049934947 1.0)))) (fma 2.0 (* 0.0001789971 (pow (* x x) 6)) (fma (fma 0.0008327945 (* x x) 0.0140005442) (pow (* x x) 4) (fma (pow x 6) 0.0694555761 (fma (pow x 4) 0.2909738639 (fma x (* x 0.7715471019) 1.0)))))))
15.0ms
(/ (sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0))))) (sqrt (fma 2.0 (* 0.0001789971 (pow (pow x 2) 6)) (fma (pow (pow x 2) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (pow x 2) 0.7715471019 1.0)))))))
8.0ms
(/ (fma (pow (* x x) 4) (fma x (* x 0.0001789971) 0.0005064034) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* x x) 0.1049934947 1.0)))) (fma 2.0 (* 0.0001789971 (pow (* x x) 6)) (fma (fma 0.0008327945 (* x x) 0.0140005442) (pow (* x x) 4) (fma (pow x 6) 0.0694555761 (fma (pow x 4) 0.2909738639 (fma x (* x 0.7715471019) 1.0))))))

series1.2s

Counts
4 → 12
Calls
4 calls:
196.0ms
(sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0)))))
387.0ms
(sqrt (/ (fma (pow (* x x) 4) (fma x (* x 0.0001789971) 0.0005064034) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* x x) 0.1049934947 1.0)))) (fma 2.0 (* 0.0001789971 (pow (* x x) 6)) (fma (fma 0.0008327945 (* x x) 0.0140005442) (pow (* x x) 4) (fma (pow x 6) 0.0694555761 (fma (pow x 4) 0.2909738639 (fma x (* x 0.7715471019) 1.0)))))))
345.0ms
(/ (sqrt (fma (fma (* 0.0001789971 x) x 0.0005064034) (pow (pow x 2) 4) (fma (pow x 6) 0.0072644182 (fma (pow x 4) 0.0424060604 (fma 0.1049934947 (pow x 2) 1.0))))) (sqrt (fma 2.0 (* 0.0001789971 (pow (pow x 2) 6)) (fma (pow (pow x 2) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (pow x 2) 0.7715471019 1.0)))))))
280.0ms
(/ (fma (pow (* x x) 4) (fma x (* x 0.0001789971) 0.0005064034) (fma 0.0072644182 (pow x 6) (fma 0.0424060604 (pow x 4) (fma (* x x) 0.1049934947 1.0)))) (fma 2.0 (* 0.0001789971 (pow (* x x) 6)) (fma (fma 0.0008327945 (* x x) 0.0140005442) (pow (* x x) 4) (fma (pow x 6) 0.0694555761 (fma (pow x 4) 0.2909738639 (fma x (* x 0.7715471019) 1.0))))))

simplify1.3s

Counts
146 → 146
Iterations
IterNodes
done5001
21953
1582
0295

prune3.3s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes88.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.7b

bsearch583.0ms

Steps
ItersRangePoint
9
0.030359728269424062
9645967.64350026
719.1299903316792
6
-219231520523.36655
-14746478108.679678
-62102401015.90998

simplify6.0ms

Iterations
IterNodes
done85
185
075

end0.0ms

sample2.8s

Algorithm
intervals
Results
2.6s8000×body80valid