Details

Time bar (total: 14.4s)

sample49.0ms

Algorithm
intervals
Results
27.0ms256×body80valid

simplify1.6s

Counts
1 → 1
Iterations

Useful iterations: done (1.6s)

IterNodesCost
044173
1132173
2596106
3305072
done500070

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.6b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x x) 0.0008327945)
0.3b
(fma 0.0001789971 (* x x) 0.0005064034)
14.7b
(* (/ (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)
28.1b
(/ (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
29×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt
17×associate-*l*
16×add-exp-log add-cbrt-cube
11×pow1
7×distribute-lft-out
6×associate-*r*
5×prod-exp cbrt-unprod
4×expm1-log1p-u pow-prod-down log1p-expm1-u associate-/l* add-log-exp
3×associate-/r* unswap-sqr
2×cbrt-undiv div-exp *-commutative div-inv associate-/l/
1×frac-2neg flip3-+ associate-*l/ clear-num flip-+ fma-udef
Counts
4 → 103
Calls
4 calls:
19.0ms
(* (* x x) 0.0008327945)
0.0ms
(fma 0.0001789971 (* x x) 0.0005064034)
27.0ms
(* (/ (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)
18.0ms
(/ (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))

series513.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* x x) 0.0008327945)
49.0ms
(fma 0.0001789971 (* x x) 0.0005064034)
246.0ms
(* (/ (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)
188.0ms
(/ (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))) (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))

simplify801.0ms

Counts
115 → 115
Iterations

Useful iterations: done (795.0ms)

IterNodesCost
02057095
14736928
215586210
done50006121

prune820.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

4.5b
(cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))
20.2b
(* (/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))) (/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)))
23.1b
(/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x))
26.9b
(/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))))

rewrite171.0ms

Algorithm
rewrite-expression-head
Rules
556×times-frac
344×add-sqr-sqrt
278×*-un-lft-identity
272×add-cube-cbrt
163×sqrt-prod
137×associate-*r*
126×cbrt-prod
50×add-exp-log
38×add-cbrt-cube
23×associate-/r*
21×unswap-sqr
20×cbrt-undiv div-exp
17×div-inv
13×prod-exp cbrt-unprod associate-/l*
11×associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-lft-out
2×frac-2neg sqrt-div clear-num associate-/r/ associate-/l/
1×frac-times flip3-+ pow1/3 associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 424
Calls
4 calls:
1.0ms
(cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))
104.0ms
(* (/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))) (/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)))
13.0ms
(/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x))
25.0ms
(/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))))

series2.4s

Counts
4 → 12
Calls
4 calls:
299.0ms
(cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))
891.0ms
(* (/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))) (/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x)))
624.0ms
(/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x))
563.0ms
(/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))))

simplify1.1s

Counts
436 → 436
Iterations

Useful iterations: done (1.1s)

IterNodesCost
086971579
1249968025
done500063469

prune3.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5))) (/ 0.2514179000665375 (pow x 3)))
0.0b
(+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5)))
0.2b
(/ 0.15298196345929327 (pow x 5))
0.3b
(/ 0.2514179000665375 (pow x 3))

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×times-frac
53×add-sqr-sqrt add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
18×fma-def
14×add-exp-log
12×cube-prod
11×add-log-exp
9×distribute-lft-out
8×add-cbrt-cube sqr-pow
6×div-exp associate-/l*
5×frac-add
4×pow1 expm1-log1p-u cube-mult unpow3 sum-log log1p-expm1-u
3×flip3-+ flip-+ div-inv
2×cbrt-undiv +-commutative pow-to-exp frac-2neg pow-exp clear-num
1×associate-+l+
Counts
4 → 169
Calls
4 calls:
238.0ms
(+ (+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5))) (/ 0.2514179000665375 (pow x 3)))
35.0ms
(+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5)))
7.0ms
(/ 0.15298196345929327 (pow x 5))
8.0ms
(/ 0.2514179000665375 (pow x 3))

series246.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(+ (+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5))) (/ 0.2514179000665375 (pow x 3)))
112.0ms
(+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5)))
47.0ms
(/ 0.15298196345929327 (pow x 5))
39.0ms
(/ 0.2514179000665375 (pow x 3))

simplify736.0ms

Counts
181 → 181
Iterations

Useful iterations: done (730.0ms)

IterNodesCost
02422148
15061875
215671800
done50001785

prune375.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes50.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 28.7b

bsearch391.0ms

Steps
ItersRangePoint
10
0.0001820196720056695
1126179.5725289274
716.1103272509417
9
-5463081689.944393
-76786.820650899
-462935.9092847789

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
054108
16594
done6594

end0.0ms

sample977.0ms

Algorithm
intervals
Results
838.0ms8000×body80valid