Details

sample68.0ms

Algorithm

intervals

Results

44.0ms

256×

body

valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	2529
11	2529
10	2182
9	1689
8	1203
7	1037
6	864
5	633
4	359
3	162
2	70
1	38
0	18

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize45.0ms

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)
3.8b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite9.0ms

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)
8.0ms	(/ 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)

series355.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
37.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
101.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
180.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify2.1s

Counts

75 → 75

Iterations

Iter	Nodes
done	5003
3	2593
2	743
1	270
0	137

prune546.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
14.1b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.1b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

80×	`add-sqr-sqrt`
58×	`times-frac`
38×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`associate-r` `associate-l`
16×	`add-cbrt-cube`
15×	`unswap-sqr`
8×	`pow1` `div-exp` `prod-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 129

Calls

4 calls:

27.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

series328.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
72.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
64.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
130.0ms	(fma (* (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify1.6s

Counts

141 → 141

Iterations

Iter	Nodes
done	5000
2	1713
1	591
0	216

prune821.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
0.5b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
3.6b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
15.5b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite21.0ms

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))
8.0ms	(/ (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)

series264.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
56.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
55.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
123.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify2.1s

Counts

143 → 143

Iterations

Iter	Nodes
done	5001
3	3517
2	1160
1	520
0	233

prune855.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

14.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.5b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(fma (/ (/ 1 (/ (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 1)) (/ (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ (/ 1 (/ (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 1)) (/ (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

series601.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
150.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
179.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))
122.0ms	(fma (/ (/ 1 (/ (* (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 1)) (/ (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304)) y)) (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) x)

simplify2.0s

Counts

65 → 65

Iterations

Iter	Nodes
done	5001
3	1638
2	527
1	204
0	96

prune544.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes457.0ms

Accuracy

98.6% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.7b

bsearch197.0ms

Steps

Iters	Range		Point
9	45027090.2690009	3906746094768.708	172322047.23901248
7	-2.1734442378507523e+44	-5.982835699292103e+42	-6.09488690648802e+42

simplify6.0ms

Iterations

Iter	Nodes
done	40
1	40
0	28

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.5s

8000×

body

valid