Details

sample36.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2006
9	1689
8	1203
7	1037
6	864
5	633
4	359
3	162
2	70
1	38
0	18

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
3.9b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.8b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
6.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

series344.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
41.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
96.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
177.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify474.0ms

Counts

75 → 75

Iterations

Iter	Nodes
done	2000
2	743
1	270
0	137

prune367.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.3b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
3.8b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
16.8b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `fma-udef`
1×	`associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 131

Calls

4 calls:

0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
11.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
4.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
0.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

series210.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
46.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
43.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
92.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify779.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	2001
2	1160
1	520
0	233

prune610.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ z 6.012459259764103) z)
0.1b	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
4.2b	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
18.3b	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
10×	`pow1` `associate-l`
9×	`associate-r`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `pow-prod-down` `-commutative` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `associate-/l/`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv` `distribute-lft-out` `associate-/l*`

Counts

4 → 100

Calls

4 calls:

28.0ms	(* (+ z 6.012459259764103) z)
22.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
65.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
42.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

series371.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (+ z 6.012459259764103) z)
94.0ms	(* (+ (* z 0.0692910599291889) 0.4917317610505968) z)
53.0ms	(* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525))
170.0ms	(/ (* y (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525)) (+ (* (+ z 6.012459259764103) z) 3.350343815022304))

simplify481.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	2001
1	582
0	204

prune529.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

8.0b	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
15.4b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.4b	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
15.4b	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
66×	`times-frac`
47×	`*-un-lft-identity` `add-cube-cbrt`
42×	`sqrt-prod`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube` `add-exp-log`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`pow1`
6×	`associate-/r*` `flip3-+` `associate-/r/` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 162

Calls

4 calls:

123.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
11.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
14.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
56.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

series420.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(* (/ y (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))) (/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))))
61.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
59.0ms	(sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304))
154.0ms	(/ (+ (* (+ (* z 0.0692910599291889) 0.4917317610505968) z) 0.279195317918525) (sqrt (+ (* (+ z 6.012459259764103) z) 3.350343815022304)))

simplify658.0ms

Counts

174 → 174

Iterations

Iter	Nodes
done	2002
1	768
0	267

prune1.0s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes328.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.1b

bsearch256.0ms

Steps

Iters	Range		Point
9	1154723.8718698514	941504501108.8118	291922397.4765716
6	-1907532089021.778	-121993772661.31783	-255355953485.46405

simplify13.0ms

Iterations

Iter	Nodes
done	42
1	42
0	30

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.5s

8000×

body

valid