Details

Time bar (total: 10.7s)

sample50.0ms

Algorithm
intervals
Results
28.0ms256×body80valid

simplify116.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
013286
161875
2334339
3500139

prune34.0ms

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: 30.8b

Counts
2 → 2

localize46.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* x x) (* 2.0 0.0001789971))
1.2b
(* (* x x) 0.0001789971)
16.0b
(/ 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))))))
26.7b
(/ (+ (+ (* (* 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)))))

rewrite71.0ms

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))))))
28.0ms
(/ (+ (+ (* (* 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)))))

series560.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (* x x) (* 2.0 0.0001789971))
26.0ms
(* (* x x) 0.0001789971)
281.0ms
(/ 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))))))
220.0ms
(/ (+ (+ (* (* 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)))))

simplify120.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
012069406
150028888

prune2.0s

Filtered
194 candidates to 158 candidates (81.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1922194
Fresh101
Picked011
Done000
Total1933196

Merged error: 0b

Counts
196 → 3

localize52.0ms

Local error

Found 4 expressions with local error:

7.1b
(cbrt (+ (+ (* (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)))))
7.1b
(cbrt (+ (+ (* (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)))))
19.4b
(/ (+ (+ (* (* 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)))) (cbrt (+ (+ (* (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))))))
27.5b
(* (* (cbrt (+ (+ (* (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))))) (cbrt (+ (+ (* (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)))))) (/ 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)))) (cbrt (+ (+ (* (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))))))))

rewrite145.0ms

Algorithm
rewrite-expression-head
Rules
204×cbrt-div
175×flip3-+ flip-+
161×times-frac
153×associate-*r/
140×frac-add
120×frac-times
98×add-sqr-sqrt
89×add-cube-cbrt *-un-lft-identity associate-*r*
60×associate-*l/
46×cbrt-prod
27×add-exp-log
25×associate-/r/
18×add-cbrt-cube
9×pow1 prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×associate-/r* associate-/l/
5×div-inv
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down associate-/l*
2×pow1/3
1×frac-2neg associate-*l* clear-num *-commutative
Counts
4 → 306
Calls
4 calls:
9.0ms
(cbrt (+ (+ (* (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)))))
14.0ms
(cbrt (+ (+ (* (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)))))
27.0ms
(/ (+ (+ (* (* 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)))) (cbrt (+ (+ (* (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))))))
68.0ms
(* (* (cbrt (+ (+ (* (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))))) (cbrt (+ (+ (* (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)))))) (/ 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)))) (cbrt (+ (+ (* (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))))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
286.0ms
(cbrt (+ (+ (* (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)))))
284.0ms
(cbrt (+ (+ (* (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)))))
443.0ms
(/ (+ (+ (* (* 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)))) (cbrt (+ (+ (* (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))))))
280.0ms
(* (* (cbrt (+ (+ (* (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))))) (cbrt (+ (+ (* (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)))))) (/ 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)))) (cbrt (+ (+ (* (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))))))))

simplify312.0ms

Algorithm
egg-herbie
Counts
318 → 318
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0243529537
1500129033

prune3.9s

Filtered
318 candidates to 271 candidates (85.2%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New3180318
Fresh011
Picked011
Done011
Total3183321

Merged error: 0b

Counts
321 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
0.0b
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
0.2b
(/ 1 (pow x 5))
0.3b
(/ 1 (pow x 3))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
57×times-frac
45×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
22×add-exp-log
19×associate-/r*
12×cube-prod div-exp
8×add-cbrt-cube sqr-pow
6×pow-to-exp rec-exp 1-exp pow-exp associate-/l*
4×pow1 expm1-log1p-u cube-mult unpow3 log1p-expm1-u add-log-exp
2×cbrt-undiv pow-flip frac-2neg clear-num fma-udef div-inv inv-pow
Counts
4 → 150
Calls
4 calls:
1.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
1.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
5.0ms
(/ 1 (pow x 5))
6.0ms
(/ 1 (pow x 3))

series246.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
117.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
42.0ms
(/ 1 (pow x 5))
37.0ms
(/ 1 (pow x 3))

simplify50.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0334806
11614643
25001634

prune235.0ms

Filtered
162 candidates to 71 candidates (43.8%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1620162
Fresh000
Picked011
Done022
Total1623165

Merged error: 0b

Counts
165 → 3

regimes52.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.2b

bsearch443.0ms

Steps
ItersRangePoint
10
0.005370866090842012
4.21737757242384e+15
28110.43447889942
8
-1822035.3400642718
-5323.7778119975
-64711.61538556859

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09547
19547

end0.0ms

sample1.0s

Algorithm
intervals
Results
900.0ms8000×body80valid