Details

Time bar (total: 18.9s)

sample62.0ms

Algorithm
intervals
Results
39.0ms256×body80valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: done (2.4s)

IterNodesCost
044173
1132173
2596106
3305072
done500070

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x x) 0.0008327945)
0.5b
(fma 0.0001789971 (* x x) 0.0005064034)
15.4b
(* (/ (+ (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)
30.1b
(/ (+ (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))))))

rewrite92.0ms

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:
18.0ms
(* (* x x) 0.0008327945)
0.0ms
(fma 0.0001789971 (* x x) 0.0005064034)
45.0ms
(* (/ (+ (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)
25.0ms
(/ (+ (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))))))

series750.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (* x x) 0.0008327945)
57.0ms
(fma 0.0001789971 (* x x) 0.0005064034)
379.0ms
(* (/ (+ (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)
280.0ms
(/ (+ (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))))))

simplify1.1s

Counts
115 → 115
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02057095
14736928
215586210
done50006121

prune1.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5))) (/ 0.2514179000665375 (pow x 3)))
0.1b
(/ 0.2514179000665375 (pow x 3))
0.2b
(/ 0.15298196345929327 (pow x 5))

rewrite446.0ms

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×pow1 expm1-log1p-u sum-log log1p-expm1-u
2×cbrt-undiv pow-to-exp frac-2neg flip3-+ pow-exp clear-num flip-+ div-inv
1×+-commutative associate-+l+
Counts
3 → 140
Calls
3 calls:
413.0ms
(+ (+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5))) (/ 0.2514179000665375 (pow x 3)))
16.0ms
(/ 0.2514179000665375 (pow x 3))
7.0ms
(/ 0.15298196345929327 (pow x 5))

series202.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(+ (+ (/ 0.5 x) (/ 0.15298196345929327 (pow x 5))) (/ 0.2514179000665375 (pow x 3)))
40.0ms
(/ 0.2514179000665375 (pow x 3))
93.0ms
(/ 0.15298196345929327 (pow x 5))

simplify1.2s

Counts
149 → 149
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02351876
14931633
215231571
done50011557

prune447.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* x x) 4)
0.3b
(fma (* x x) 0.0008327945 0.0140005442)
0.5b
(fma 0.0001789971 (* x x) 0.0005064034)
30.1b
(* (+ (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))) (/ x (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)))))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
15×*-un-lft-identity
14×pow1
13×add-cube-cbrt associate-*r*
12×add-exp-log
10×times-frac
9×add-cbrt-cube
6×pow-pow
4×expm1-log1p-u associate-*l* log1p-expm1-u add-log-exp
3×pow-unpow prod-exp
2×frac-times flip3-+ pow-prod-down associate-*l/ pow-exp cbrt-unprod flip-+ fma-udef unswap-sqr
1×cbrt-undiv pow2 pow-to-exp unpow-prod-down pow-plus associate-*r/ div-exp pow-sqr *-commutative pow-prod-up div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
6.0ms
(pow (* x x) 4)
0.0ms
(fma (* x x) 0.0008327945 0.0140005442)
0.0ms
(fma 0.0001789971 (* x x) 0.0005064034)
50.0ms
(* (+ (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))) (/ x (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)))))))

series637.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(pow (* x x) 4)
97.0ms
(fma (* x x) 0.0008327945 0.0140005442)
73.0ms
(fma 0.0001789971 (* x x) 0.0005064034)
390.0ms
(* (+ (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))) (/ x (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)))))))

simplify1.1s

Counts
94 → 94
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01923862
14273559
215453135
done50023096

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize96.0ms

Local error

Found 4 expressions with local error:

6.7b
(cbrt (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)))))
15.4b
(* (* (* (cbrt (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 (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 (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))))) (fma 0.0001789971 (* 2.0 (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)
23.9b
(/ (cbrt (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))))) (fma 0.0001789971 (* 2.0 (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))))))
28.4b
(* (* (cbrt (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 (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 (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))))) (fma 0.0001789971 (* 2.0 (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)))))))

rewrite208.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
36×add-exp-log
34×add-cube-cbrt *-un-lft-identity
25×cbrt-prod associate-*r*
23×add-cbrt-cube
18×pow1
17×prod-exp cbrt-unprod
9×pow-prod-down
6×associate-/l*
5×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r* unswap-sqr
2×associate-*r/ associate-*l* *-commutative div-inv
1×frac-2neg pow1/3 associate-*l/ clear-num
Counts
4 → 129
Calls
4 calls:
2.0ms
(cbrt (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)))))
141.0ms
(* (* (* (cbrt (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 (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 (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))))) (fma 0.0001789971 (* 2.0 (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)
6.0ms
(/ (cbrt (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))))) (fma 0.0001789971 (* 2.0 (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))))))
50.0ms
(* (* (cbrt (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 (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 (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))))) (fma 0.0001789971 (* 2.0 (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)))))))

series1.7s

Counts
4 → 12
Calls
4 calls:
436.0ms
(cbrt (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)))))
320.0ms
(* (* (* (cbrt (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 (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 (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))))) (fma 0.0001789971 (* 2.0 (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
(/ (cbrt (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))))) (fma 0.0001789971 (* 2.0 (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))))))
333.0ms
(* (* (cbrt (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 (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 (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))))) (fma 0.0001789971 (* 2.0 (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)))))))

simplify2.3s

Counts
141 → 141
Iterations

Useful iterations: done (2.3s)

IterNodesCost
031117162
178316753
2280511219
done500110700

prune1.6s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes89.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 32.0b

bsearch519.0ms

Steps
ItersRangePoint
9
110.15968793260775
1173724448.4928873
759.2756960152701
9
-3484513403575543.0
-66911392.43097515
-2189916760047.7583

simplify28.0ms

Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
053107
16293
done6293

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.1s8000×body80valid