Details

Time bar (total: 8.9s)

sample43.0ms

Algorithm
intervals
Results
23.0ms256×body80valid

simplify113.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
013286
161875
2334339
3500139

prune27.0ms

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: 29.9b

Counts
2 → 2

localize43.0ms

Local error

Found 4 expressions with local error:

0.8b
(* (* x x) (* 2.0 0.0001789971))
0.8b
(* (* x x) 0.0001789971)
13.8b
(/ 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))))))
25.9b
(/ (+ (+ (* (* 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)))))

rewrite458.0ms

Algorithm
rewrite-expression-head
Rules
2182×*-un-lft-identity
1228×distribute-lft-out
822×times-frac
794×associate-*l*
277×add-sqr-sqrt
236×add-cube-cbrt
127×associate-/r*
59×associate-/r/
35×flip3-+ flip-+
28×add-exp-log associate-*r/ frac-add add-cbrt-cube
26×unswap-sqr
25×associate-/l*
24×associate-*r*
21×pow1
12×associate-/l/
11×pow-prod-down prod-exp cbrt-unprod
9×swap-sqr
8×*-commutative
6×div-inv
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
Counts
4 → 727
Calls
4 calls:
13.0ms
(* (* x x) (* 2.0 0.0001789971))
8.0ms
(* (* x x) 0.0001789971)
188.0ms
(/ 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))))))
173.0ms
(/ (+ (+ (* (* 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)))))

series567.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (* x x) (* 2.0 0.0001789971))
25.0ms
(* (* x x) 0.0001789971)
287.0ms
(/ 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))))))
227.0ms
(/ (+ (+ (* (* 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)))))

simplify309.0ms

Algorithm
egg-herbie
Counts
739 → 739
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0145329551
1500128234

prune2.1s

Filtered
739 candidates to 205 candidates (27.7%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New7354739
Fresh101
Picked101
Done000
Total7374741

Merged error: 0.0b

Counts
741 → 4

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.17858401087518094 (pow x 4) 1.0)
1.6b
(/ x (fma 0.6665536072 (pow x 2) (fma 0.17858401087518094 (pow x 4) 1.0)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
Counts
2 → 39
Calls
2 calls:
1.0ms
(fma 0.17858401087518094 (pow x 4) 1.0)
3.0ms
(/ x (fma 0.6665536072 (pow x 2) (fma 0.17858401087518094 (pow x 4) 1.0)))

series200.0ms

Counts
2 → 6
Calls
2 calls:
86.0ms
(fma 0.17858401087518094 (pow x 4) 1.0)
113.0ms
(/ x (fma 0.6665536072 (pow x 2) (fma 0.17858401087518094 (pow x 4) 1.0)))

simplify92.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0171342
1597312
22755310
35002310

prune117.0ms

Filtered
45 candidates to 36 candidates (80.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New45045
Fresh033
Picked011
Done000
Total45449

Merged error: 0.0b

Counts
49 → 4

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 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)))))
0.6b
(* (* x x) 0.0140005442)
0.8b
(* (* x x) (* 2.0 0.0001789971))
28.9b
(* (/ 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))))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* 0.0001789971 x) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

rewrite270.0ms

Algorithm
rewrite-expression-head
Rules
228×*-un-lft-identity
162×associate-*l*
112×distribute-lft-out
98×add-sqr-sqrt
67×times-frac
52×add-cube-cbrt
28×add-exp-log add-cbrt-cube unswap-sqr
27×associate-*r*
23×pow1
22×associate-/r*
17×associate-*l/
13×prod-exp cbrt-unprod
12×pow-prod-down associate-/r/
10×flip3-+ flip-+
9×swap-sqr *-commutative
8×associate-*r/ frac-add
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cbrt-undiv frac-2neg div-exp clear-num fma-udef div-inv
1×distribute-rgt-in distribute-lft-in
Counts
4 → 247
Calls
4 calls:
113.0ms
(/ 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)))))
8.0ms
(* (* x x) 0.0140005442)
13.0ms
(* (* x x) (* 2.0 0.0001789971))
123.0ms
(* (/ 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))))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* 0.0001789971 x) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

series539.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(/ 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)))))
30.0ms
(* (* x x) 0.0140005442)
26.0ms
(* (* x x) (* 2.0 0.0001789971))
300.0ms
(* (/ 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))))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* 0.0001789971 x) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

simplify88.0ms

Algorithm
egg-herbie
Counts
259 → 259
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
010035500
150025071

prune1.5s

Filtered
259 candidates to 138 candidates (53.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2572259
Fresh202
Picked011
Done101
Total2603263

Merged error: 0.0b

Counts
263 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.265709700396151 (pow x 5))
0.1b
(* 0.6665536072 (pow x 3))
20.4b
(- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
409×add-sqr-sqrt
342×prod-diff
299×associate-*r*
169×*-un-lft-identity
168×unpow-prod-down
161×add-cube-cbrt
144×unswap-sqr
124×associate-*l*
88×sqr-pow
40×*-commutative
19×unpow3
18×fma-neg
16×difference-of-squares
13×add-exp-log
7×pow1 add-cbrt-cube
6×prod-exp
5×add-log-exp
4×distribute-lft-out--
3×expm1-log1p-u log1p-expm1-u
2×pow-to-exp pow-prod-down pow-exp cbrt-unprod
1×sub-neg flip3-- diff-log flip--
Counts
3 → 451
Calls
3 calls:
6.0ms
(* 0.265709700396151 (pow x 5))
9.0ms
(* 0.6665536072 (pow x 3))
30.0ms
(- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3)))

series240.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(* 0.265709700396151 (pow x 5))
42.0ms
(* 0.6665536072 (pow x 3))
150.0ms
(- (* 0.265709700396151 (pow x 5)) (* 0.6665536072 (pow x 3)))

simplify165.0ms

Algorithm
egg-herbie
Counts
460 → 460
Iterations

Useful iterations: 2 (90.0ms)

IterNodesCost
011668246
130834985
250014983

prune330.0ms

Filtered
460 candidates to 106 candidates (23.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New4600460
Fresh011
Picked011
Done011
Total4603463

Merged error: 0.0b

Counts
463 → 3

regimes39.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 28.3b

bsearch659.0ms

Steps
ItersRangePoint
10
1.0482644148039984e-06
3857898261607.3584
1020.6821270644334
10
-1556119314.230081
-0.05767290693153419
-3296.9186793635513

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09245
19645
29645

end0.0ms

sample825.0ms

Algorithm
intervals
Results
725.0ms8000×body80valid