Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify83.0ms

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: 17.4b

Counts

2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
4.7b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.9b	(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)
25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
61.0ms	(/ 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)

simplify102.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (95.0ms)

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

prune233.0ms

Filtered

71 candidates to 59 candidates (83.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	67	4	71
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	6	73

Merged error: 0.0b

Counts

73 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
0.4b	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
4.8b	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
16.9b	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
7.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
1.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series258.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
37.0ms	(/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))
63.0ms	(* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304)))
133.0ms	(fma (* y (/ 1 (fma (+ z 6.012459259764103) z 3.350343815022304))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify54.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	364	632
1	1472	543
2	5001	514

prune250.0ms

Filtered

103 candidates to 68 candidates (66.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

1.9b	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
4.7b	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
16.8b	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
16.9b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

2.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
5.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
1.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
1.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series286.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
65.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
69.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
132.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify132.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	352	720
1	1070	618
2	4365	587
3	5001	583

prune279.0ms

Filtered

94 candidates to 68 candidates (72.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	94	6	100

Merged error: 0.0b

Counts

100 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
16.9b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
16.9b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
16.9b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite10.0ms

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:

7.0ms	(/ 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)
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
1.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

series466.0ms

Counts

4 → 12

Calls

4 calls:

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)
138.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
132.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify95.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (87.0ms)

Iter	Nodes	Cost
0	209	520
1	674	461
2	2867	456
3	5001	450

prune293.0ms

Filtered

71 candidates to 62 candidates (87.3%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	71	6	77

Merged error: 0.0b

Counts

77 → 6

regimes167.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.8b

bsearch146.0ms

Steps

Iters	Range		Point
8	6.042829624826513e-05	0.09081442282169057	0.08953599064961001
10	-2.898468026705626e+24	-29213333872915.715	-29527194556645.625

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample585.0ms

Algorithm

intervals

Results

403.0ms

8000×

body

valid

Details

sample24.0ms

simplify83.0ms

prune9.0ms

localize13.0ms

rewrite6.0ms

series238.0ms

simplify102.0ms

prune233.0ms

localize13.0ms

rewrite14.0ms

series258.0ms

simplify54.0ms

prune250.0ms

localize21.0ms

rewrite11.0ms

series286.0ms

simplify132.0ms

prune279.0ms

localize16.0ms

rewrite10.0ms

series466.0ms

simplify95.0ms

prune293.0ms

regimes167.0ms

bsearch146.0ms

simplify1.0ms

end0.0ms

sample585.0ms

Profiling