Details

Time bar (total: 10.3s)

sample49.0ms

Algorithm
intervals
Results
25.0ms256×body80valid

simplify114.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (24.0ms)

IterNodesCost
013286
161875
2334339
3500139

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x x) 0.0001789971)
0.3b
(* (* x x) 0.0072644182)
15.3b
(/ 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))))))
26.2b
(/ (+ (+ (* (* 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)))))

rewrite1.2s

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:
19.0ms
(* (* x x) 0.0001789971)
17.0ms
(* (* x x) 0.0072644182)
391.0ms
(/ 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))))))
755.0ms
(/ (+ (+ (* (* 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)))))

series505.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(* (* x x) 0.0001789971)
26.0ms
(* (* x x) 0.0072644182)
256.0ms
(/ 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))))))
200.0ms
(/ (+ (+ (* (* 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)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
191 → 191
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011679359
150028847

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* x x) 3)
0.3b
(* (* x x) 0.0140005442)
0.3b
(* (* x x) (* 2.0 0.0001789971))
29.9b
(* (/ 1 (+ (+ (* (* 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))))) (* x (* 1 (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))

rewrite849.0ms

Algorithm
rewrite-expression-head
Rules
76×add-exp-log
48×prod-exp
45×add-cbrt-cube
38×pow1
24×cbrt-unprod
21×associate-*l*
18×pow-prod-down
14×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
12×distribute-rgt-in distribute-lft-in
9×times-frac
8×1-exp div-exp fma-udef
6×pow-pow associate-/r/
5×flip3-+ associate-*r* flip-+
4×expm1-log1p-u rec-exp associate-*r/ frac-add log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow *-commutative
2×pow-exp rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod associate-*l/ pow-sqr pow-prod-up div-inv unswap-sqr sqr-pow
Counts
4 → 137
Calls
4 calls:
6.0ms
(pow (* x x) 3)
17.0ms
(* (* x x) 0.0140005442)
26.0ms
(* (* x x) (* 2.0 0.0001789971))
794.0ms
(* (/ 1 (+ (+ (* (* 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))))) (* x (* 1 (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(pow (* x x) 3)
23.0ms
(* (* x x) 0.0140005442)
30.0ms
(* (* x x) (* 2.0 0.0001789971))
262.0ms
(* (/ 1 (+ (+ (* (* 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))))) (* x (* 1 (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))))

simplify146.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09233414
149332664
250012664

prune947.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(pow (* x x) 3)
0.3b
(fma (* (* x x) 2.0) 0.0001789971 0.0008327945)
15.3b
(/ x (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 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)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)))))
26.2b
(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 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)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
55×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/r*
14×add-exp-log add-cbrt-cube
12×pow1
6×pow-pow div-inv associate-/l*
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×pow-unpow
2×frac-2neg pow-exp clear-num rem-cube-cbrt
1×pow2 cube-mult pow-to-exp unpow-prod-down pow-plus unpow3 cube-prod pow-prod-down prod-exp associate-/r/ pow-sqr pow-prod-up cbrt-unprod fma-udef sqr-pow
Counts
4 → 139
Calls
4 calls:
8.0ms
(pow (* x x) 3)
0.0ms
(fma (* (* x x) 2.0) 0.0001789971 0.0008327945)
8.0ms
(/ x (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 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)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)))))
5.0ms
(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 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)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

series555.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(pow (* x x) 3)
57.0ms
(fma (* (* x x) 2.0) 0.0001789971 0.0008327945)
262.0ms
(/ x (/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 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)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)))))
196.0ms
(/ (fma (pow x 6) (fma x (* x 0.0140005442) 0.0694555761) (fma (fma (* (* x x) 2.0) 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)))) (fma (pow x 4) (fma x (* x 0.0072644182) 0.0424060604) (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))))

simplify118.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05835241
126264910
250014880

prune1.4s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

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 x)))
0.0b
(fma 0.15298196345929327 (/ 1 (pow x 5)) (/ 0.5 x))
0.1b
(/ 1 (pow x 3))
0.2b
(/ 1 (pow x 5))

rewrite22.0ms

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 x)))
0.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (/ 0.5 x))
8.0ms
(/ 1 (pow x 3))
8.0ms
(/ 1 (pow x 5))

series234.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(fma 0.2514179000665375 (/ 1 (pow x 3)) (fma 0.15298196345929327 (/ 1 (pow x 5)) (/ 0.5 x)))
107.0ms
(fma 0.15298196345929327 (/ 1 (pow x 5)) (/ 0.5 x))
29.0ms
(/ 1 (pow x 3))
45.0ms
(/ 1 (pow x 5))

simplify41.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0337768
11590603
25001603

prune270.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes33.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.0b

bsearch403.0ms

Steps
ItersRangePoint
8
9.114942375872904
154062.39550417996
585.2479772194044
9
-1146855530477.335
-15077057.36594219
-4293930135.7553926

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08040
18440
28440

end0.0ms

sample903.0ms

Algorithm
intervals
Results
771.0ms8000×body80valid