Details

Time bar (total: 13.8s)

sample42.0ms

Algorithm
intervals
Results
22.0ms256×body80valid

simplify111.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
013286
161875
2334339
3500139

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* x x) 0.0072644182)
0.4b
(* (* x x) 0.0140005442)
15.4b
(/ 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))))))
25.2b
(/ (+ (+ (* (* 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)))))

rewrite749.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
64×add-sqr-sqrt
62×add-cube-cbrt *-un-lft-identity
31×associate-/r/
30×flip3-+ flip-+
24×associate-*r/ frac-add
22×associate-/r*
21×add-exp-log add-cbrt-cube
14×pow1
6×associate-*r* pow-prod-down prod-exp cbrt-unprod div-inv associate-/l/ associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg associate-*l* clear-num *-commutative unswap-sqr
Counts
4 → 179
Calls
4 calls:
7.0ms
(* (* x x) 0.0072644182)
9.0ms
(* (* x x) 0.0140005442)
248.0ms
(/ 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))))))
478.0ms
(/ (+ (+ (* (* 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)))))

series529.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(* (* x x) 0.0072644182)
24.0ms
(* (* x x) 0.0140005442)
271.0ms
(/ 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))))))
207.0ms
(/ (+ (+ (* (* 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)))))

simplify109.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011609359
150028847

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945)
0.3b
(* (* x x) 0.0001789971)
0.4b
(* (* x x) 0.0072644182)
28.8b
(/ (/ x (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))))) (/ 1 (+ (+ (* (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))))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
553×times-frac
246×add-sqr-sqrt
244×add-cube-cbrt *-un-lft-identity
85×associate-/r/
70×flip3-+ flip-+
56×associate-*r/ frac-add
36×add-exp-log
35×div-inv
26×add-cbrt-cube
19×associate-/r*
16×div-exp
14×pow1
13×associate-/l*
8×cbrt-undiv
6×associate-*r* pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp 1-exp associate-*l* *-commutative unswap-sqr
1×frac-2neg clear-num fma-udef associate-/l/
Counts
4 → 357
Calls
4 calls:
0.0ms
(fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945)
11.0ms
(* (* x x) 0.0001789971)
7.0ms
(* (* x x) 0.0072644182)
40.0ms
(/ (/ x (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))))) (/ 1 (+ (+ (* (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))))))

series394.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945)
24.0ms
(* (* x x) 0.0001789971)
31.0ms
(* (* x x) 0.0072644182)
280.0ms
(/ (/ x (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* 2.0 (pow x 2)) 0.0001789971 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))))) (/ 1 (+ (+ (* (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))))))

simplify263.0ms

Algorithm
egg-herbie
Counts
369 → 369
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0221824081
1500323140

prune3.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 2.0 (pow x 2)) 0.0001789971)
0.3b
(* (* x x) 0.0001789971)
0.4b
(* (* x x) 0.0072644182)
28.8b
(/ (/ x (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (+ (* (* 2.0 (pow x 2)) 0.0001789971) 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))))) (/ 1 (+ (+ (* (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))))))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
553×times-frac
247×add-sqr-sqrt
245×add-cube-cbrt *-un-lft-identity
85×associate-/r/
70×flip3-+ flip-+
56×associate-*r/ frac-add
46×add-exp-log
35×div-inv
31×add-cbrt-cube
19×associate-/r*
16×pow1 div-exp
13×prod-exp associate-/l*
9×associate-*r* cbrt-unprod
8×cbrt-undiv
7×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*l* *-commutative
2×rec-exp 1-exp unswap-sqr
1×pow-to-exp frac-2neg pow-exp clear-num associate-/l/
Counts
4 → 368
Calls
4 calls:
9.0ms
(* (* 2.0 (pow x 2)) 0.0001789971)
11.0ms
(* (* x x) 0.0001789971)
7.0ms
(* (* x x) 0.0072644182)
39.0ms
(/ (/ x (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (+ (* (* 2.0 (pow x 2)) 0.0001789971) 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))))) (/ 1 (+ (+ (* (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))))))

series362.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(* (* 2.0 (pow x 2)) 0.0001789971)
24.0ms
(* (* x x) 0.0001789971)
24.0ms
(* (* x x) 0.0072644182)
284.0ms
(/ (/ x (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (+ (* (* 2.0 (pow x 2)) 0.0001789971) 0.0008327945) (* x (* (pow (* x x) 3) (pow x 3))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))))) (/ 1 (+ (+ (* (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))))))

simplify263.0ms

Algorithm
egg-herbie
Counts
380 → 380
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0229324674
1500123718

prune3.6s

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
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
0.0b
(/ 1 (pow x 5))
0.1b
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
0.5b
(/ 1 (pow x 3))

rewrite14.0ms

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:
0.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
4.0ms
(/ 1 (pow x 5))
0.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
5.0ms
(/ 1 (pow x 3))

series245.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x))))
41.0ms
(/ 1 (pow x 5))
117.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (* 0.5 (/ 1 x)))
31.0ms
(/ 1 (pow x 3))

simplify42.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0334792
11614629
25001620

prune261.0ms

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 29.3b

bsearch417.0ms

Steps
ItersRangePoint
9
15.365363555117188
8982319.97820102
341298.60975052114
9
-152849402421631.16
-48882.64719934817
-11921922.190530011

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09145
19145

end0.0ms

sample825.0ms

Algorithm
intervals
Results
720.0ms8000×body80valid