Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify84.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 17.1b

Counts

2 → 2

localize12.0ms

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)
2.3b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.8b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite6.0ms

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:

1.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series238.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
28.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
58.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
133.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify103.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (96.0ms)

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

prune248.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	68	5	73

Merged error: 0.0b

Counts

73 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.6b	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
2.2b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
16.8b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
6.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
3.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
1.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series192.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
41.0ms	(/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y))
41.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
85.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify62.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	475	1087
1	1998	960
2	5002	880

prune349.0ms

Filtered

139 candidates to 86 candidates (61.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	139	5	144

Merged error: 0.0b

Counts

144 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
15.9b	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
15.9b	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
16.8b	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 69

Calls

4 calls:

3.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
1.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
1.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
1.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

series296.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)
85.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
84.0ms	(sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
85.0ms	(fma (/ 1 (/ (fma (+ z 6.012459259764103) z 3.350343815022304) y)) (* (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (sqrt (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))) x)

simplify120.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	283	598
1	842	538
2	4208	517
3	5001	511

prune306.0ms

Filtered

81 candidates to 66 candidates (81.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	81	5	86

Merged error: 0.0b

Counts

86 → 5

localize12.0ms

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)
0.1b	(* (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y)
16.6b	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 83

Calls

4 calls:

1.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
9.0ms	(* (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y)
3.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series193.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
30.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
77.0ms	(* (/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y)
67.0ms	(/ (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify41.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	311	696
1	1066	613
2	5001	610

prune302.0ms

Filtered

95 candidates to 76 candidates (80.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	1	1
Picked	0	1	1
Done	1	2	3
Total	95	5	100

Merged error: 0b

Counts

100 → 5

regimes126.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 15.8b

bsearch141.0ms

Steps

Iters	Range		Point
9	13523.20185778739	10938932741.588787	202060117.1853226
9	-1.030890742424049e+20	-431362558525.3461	-480137818217515.2

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	9
1	28	9

end0.0ms

sample483.0ms

Algorithm

intervals

Results

320.0ms

8000×

body

valid