Details

sample28.0ms

Algorithm

intervals

Results

15.0ms

256×

body

valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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: 14.9b

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)
3.9b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.0b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

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)

series231.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
27.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
57.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
129.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify107.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (100.0ms)

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

prune226.0ms

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

localize16.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
15.0b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
15.0b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
15.0b	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite7.0ms

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:

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)
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)

series442.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ y (fma (+ z 6.012459259764103) z 3.350343815022304))
130.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
126.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)
129.0ms	(fma (/ y (fma (+ z 6.012459259764103) z 3.350343815022304)) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify96.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (88.0ms)

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

prune296.0ms

Filtered

71 candidates to 62 candidates (87.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Merged error: 0.0b

Counts

77 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.7b	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
3.9b	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
14.3b	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
15.0b	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

rewrite12.0ms

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)

series274.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))
57.0ms	(/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304))))
67.0ms	(log (fma (+ z 6.012459259764103) z 3.350343815022304))
130.0ms	(fma (/ y (exp (log (fma (+ z 6.012459259764103) z 3.350343815022304)))) (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525) x)

simplify138.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (123.0ms)

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

prune263.0ms

Filtered

94 candidates to 67 candidates (71.3%)

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304)) x)
0.1b	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.1b	(* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
19.9b	(/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt`
7×	`fma-def`
6×	`pow1` `times-frac` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `associate-/r*` `fma-udef`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

6.0ms	(+ (/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304)) x)
1.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
3.0ms	(* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
4.0ms	(/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304))

series320.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ (/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304)) x)
24.0ms	(fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)
49.0ms	(* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525))
105.0ms	(/ (* y (fma (fma z 0.0692910599291889 0.4917317610505968) z 0.279195317918525)) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	331	569
1	1407	492
2	5001	488

prune216.0ms

Filtered

88 candidates to 67 candidates (76.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	1	2
Picked	0	1	1
Done	0	3	3
Total	88	6	94

Merged error: 0b

Counts

94 → 6

regimes163.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 16.6b

bsearch166.0ms

Steps

Iters	Range		Point
9	1.70242804785995e-07	1.2368608357549227	1.2145866554018125
10	-4.658417396193765e+26	-8.40989481376761e+16	-1.0344148084450786e+17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	10
1	31	10

end0.0ms

sample600.0ms

Algorithm

intervals

Results

415.0ms

8000×

body

valid