Details

Time bar (total: 25.6s)

sample113.0ms

Algorithm
intervals
Results
73.0ms256×body80valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: done (2.6s)

IterNodesCost
044173
1132173
2608106
3348072
done500071

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize123.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* x x) 0.0008327945)
0.4b
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
13.4b
(/ x (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
25.9b
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
114×times-frac
97×*-un-lft-identity
66×add-sqr-sqrt
65×add-cube-cbrt
22×associate-/r*
16×add-exp-log add-cbrt-cube distribute-lft-out
11×associate-/r/
9×pow1
6×div-inv associate-/l*
5×flip3-+ flip-+
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×frac-2neg clear-num
1×associate-*l* *-commutative fma-udef unswap-sqr
Counts
4 → 158
Calls
4 calls:
19.0ms
(* (* x x) 0.0008327945)
0.0ms
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
34.0ms
(/ x (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
22.0ms
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))

series726.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (* x x) 0.0008327945)
79.0ms
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
347.0ms
(/ x (/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))
258.0ms
(/ (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (+ (fma (pow x 6) 0.0072644182 (* (pow (* x x) 4) (+ (* 0.0001789971 (* x x)) 0.0005064034))) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))

simplify2.9s

Counts
170 → 170
Iterations

Useful iterations: done (2.9s)

IterNodesCost
029914775
176714413
2433913450
done500213287

prune2.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize94.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* x x) 0.0008327945)
0.4b
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
13.4b
(/ x (* (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))))
25.9b
(* (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
33×add-exp-log
23×add-sqr-sqrt add-cbrt-cube
16×*-un-lft-identity associate-*r*
15×add-cube-cbrt
14×times-frac
11×pow1 prod-exp
9×div-exp
7×cbrt-unprod
5×cbrt-undiv
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×associate-/l*
2×rec-exp 1-exp associate-*r/ associate-/r/ un-div-inv *-commutative div-inv
1×frac-2neg clear-num associate-/r* fma-udef
Counts
4 → 98
Calls
4 calls:
19.0ms
(* (* x x) 0.0008327945)
0.0ms
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
23.0ms
(/ x (* (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))))
30.0ms
(* (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))))

series788.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* (* x x) 0.0008327945)
66.0ms
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
390.0ms
(/ x (* (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0)))))))
294.0ms
(* (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ 0.0140005442 (* (* x x) 0.0008327945)) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))))

simplify3.0s

Counts
110 → 110
Iterations

Useful iterations: 2 (647.0ms)

IterNodesCost
02246376
15476176
230995068
done50005068

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize108.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma 0.0001789971 (pow x 2) 0.0005064034)
0.4b
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
0.7b
(/ x (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))
28.3b
(/ (/ x (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
430×times-frac
208×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
30×div-inv
28×add-exp-log
18×add-cbrt-cube
17×div-exp
16×associate-/r* associate-/l*
9×cbrt-undiv
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num fma-udef
1×associate-/r/ associate-/l/
Counts
4 → 270
Calls
4 calls:
1.0ms
(fma 0.0001789971 (pow x 2) 0.0005064034)
1.0ms
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
10.0ms
(/ x (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))
36.0ms
(/ (/ x (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))))

series695.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma 0.0001789971 (pow x 2) 0.0005064034)
62.0ms
(fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))
218.0ms
(/ x (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0))))))
316.0ms
(/ (/ x (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma 0.0008327945 (* x x) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (/ 1 (fma (pow x 6) 0.0072644182 (fma (fma 0.0001789971 (pow x 2) 0.0005064034) (pow (* x x) 4) (fma (pow x 4) 0.0424060604 (fma (* x x) 0.1049934947 1.0))))))

simplify1.1s

Counts
282 → 282
Iterations

Useful iterations: done (1.0s)

IterNodesCost
051730692
1158529987
done500028629

prune2.6s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite516.0ms

Algorithm
rewrite-expression-head
Rules
85×times-frac
83×*-un-lft-identity
60×add-sqr-sqrt add-cube-cbrt
33×unpow-prod-down
30×fma-def
19×associate-/r*
14×add-exp-log
12×cube-prod
11×add-log-exp sqr-pow
9×distribute-lft-out
8×add-cbrt-cube
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 → 181
Calls
4 calls:
408.0ms
(+ (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)) (/ 0.2514179000665375 (pow x 3)))
78.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
8.0ms
(/ 0.2514179000665375 (pow x 3))
8.0ms
(/ 0.15298196345929327 (pow x 5))

series411.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ (+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x)) (/ 0.2514179000665375 (pow x 3)))
184.0ms
(+ (/ 0.15298196345929327 (pow x 5)) (/ 0.5 x))
81.0ms
(/ 0.2514179000665375 (pow x 3))
71.0ms
(/ 0.15298196345929327 (pow x 5))

simplify1.5s

Counts
193 → 193
Iterations

Useful iterations: 2 (623.0ms)

IterNodesCost
02422146
15501873
224821788
done50001788

prune868.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes98.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.4b

bsearch769.0ms

Steps
ItersRangePoint
11
9.093534403752284e-26
13730598.322931442
671.5554191952253
9
-2.408385263222486e+28
-1.1941517926520358e+22
-3.766647159172341e+25

simplify17.0ms

Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
056108
16494
done6494

end0.0ms

sample2.9s

Algorithm
intervals
Results
2.6s8000×body80valid