Details

sample22.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify85.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	38	7
1	72	7
2	167	6
3	354	6
4	646	6
5	921	6
6	1060	6
7	1331	6
8	1792	6
9	1860	6
10	1861	6
11	1861	6

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.7b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
2.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
0.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series241.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
26.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
63.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
132.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify109.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	245	408
1	760	361
2	3482	358
3	5001	356

prune258.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

258×	`times-frac`
145×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
138×	`sqrt-prod`
22×	`associate-/l*`
9×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
6×	`pow1` `associate-/r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`

Counts

4 → 217

Calls

4 calls:

14.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (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 (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series512.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))
257.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
57.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
138.0ms	(fma (/ (/ y (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify83.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	714	3355
1	2634	2956
2	5001	2888

prune547.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.7b	(fma (* (* (/ 1/2 (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ 2 (pow (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 3))) (/ y (* (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

1.0ms	(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 (* (* (/ 1/2 (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ 2 (pow (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 3))) (/ y (* (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series246.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
54.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
51.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
87.0ms	(fma (* (* (/ 1/2 (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) (/ 2 (pow (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) 3))) (/ y (* (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify84.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	176	619
1	573	553
2	2889	542
3	5001	512

prune355.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

12.8b	(* (/ (* (/ 1 (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) y) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
14.7b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.2b	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
33×	`add-sqr-sqrt`
30×	`add-cbrt-cube`
26×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r`
20×	`div-exp` `prod-exp`
13×	`cbrt-prod`
12×	`cbrt-undiv` `cbrt-unprod`
10×	`associate-l`
9×	`sqrt-prod`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `div-inv`
1×	`frac-times` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 112

Calls

4 calls:

36.0ms	(* (/ (* (/ 1 (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) y) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (cbrt (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))
1.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))

series290.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ (* (/ 1 (cbrt (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))) y) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))) (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))))
54.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
51.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
108.0ms	(cbrt (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify99.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	722	1793
1	3466	1535
2	5002	1512

prune486.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 16.8b

bsearch145.0ms

Steps

Iters	Range		Point
9	0.0005333266348582408	74219.82001652327	72489.24391222252
10	-7.995242360819531e+16	-1842.5261786401543	-897232587.5004816

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	9
1	28	9

end0.0ms

sample479.0ms

Algorithm

intervals

Results

307.0ms

8000×

body

valid