Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	195×	body	80	valid
3.0ms	27×	body	640	valid
1.0ms	18×	body	320	valid
1.0ms	9×	body	1280	valid
0.0ms	7×	body	160	valid

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (20.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	76	5
3	137	5
4	285	4
5	459	4
6	719	4
7	848	4
8	1064	4
9	1397	4
10	2101	4
11	5002	4

prune7.0ms

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: 14.5b

Counts

2 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.5b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
12×	`times-frac`
11×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `distribute-lft-out`
3×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`

Counts

2 → 45

Calls

2 calls:

6.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series107.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ y (+ y 1.0))
68.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify167.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (160.0ms)

Iter	Nodes	Cost
0	202	264
1	705	238
2	3124	232
3	5002	228

prune120.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	42	9	51
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	44	9	53

Merged error: 8.1b

Counts

53 → 9

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ y 1.0))
0.1b	(* y (/ 1 (+ y 1.0)))
4.0b	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
16×	`add-exp-log`
10×	`associate-*r/` `add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out`
7×	`associate-/l*`
6×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`expm1-log1p-u` `associate-l` `clear-num` `un-div-inv` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `frac-2neg` `flip3-+` `1-exp` `cbrt-unprod` `flip-+` `div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

3 → 103

Calls

3 calls:

6.0ms	(/ 1 (+ y 1.0))
12.0ms	(* y (/ 1 (+ y 1.0)))
1.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

series131.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(/ 1 (+ y 1.0))
38.0ms	(* y (/ 1 (+ y 1.0)))
67.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	330	517
1	1460	441
2	5002	391

prune175.0ms

Filtered

112 candidates to 68 candidates (60.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 8.1b

Counts

121 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
11.0b	(fma (* (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt 1) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
1.0ms	(fma (* (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt 1) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series387.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(cbrt (+ y 1.0))
103.0ms	(cbrt (+ y 1.0))
104.0ms	(cbrt (+ y 1.0))
68.0ms	(fma (* (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt 1) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify115.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	233	578
1	689	527
2	2524	512
3	5001	483

prune246.0ms

Filtered

70 candidates to 63 candidates (90.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	68	10	78

Merged error: 8.1b

Counts

78 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (cbrt (+ y 1.0)))
10.5b	(fma (* (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (/ (cbrt 1) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

19×	`cbrt-prod`
14×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (cbrt (+ y 1.0)))
1.0ms	(fma (* (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (/ (cbrt 1) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series388.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (+ y 1.0))
107.0ms	(cbrt (+ y 1.0))
107.0ms	(cbrt (cbrt (+ y 1.0)))
67.0ms	(fma (* (/ y (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (/ (cbrt 1) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify179.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (161.0ms)

Iter	Nodes	Cost
0	360	730
1	1089	661
2	4291	639
3	5001	616

prune285.0ms

Filtered

73 candidates to 65 candidates (89.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 8.1b

Counts

83 → 10

regimes108.0ms

Accuracy

94.5% (0.4b remaining)

Error of 7.3b against oracle of 6.9b and baseline of 14.7b

bsearch90.0ms

Steps

Iters	Range		Point
9	3.0899898012220906e+94	1.4363513444191874e+100	3.1206105927613924e+94
7	-861769003990319.9	-21436759175312.676	-850087197437636.9

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample459.0ms

Algorithm

intervals

Results

163.0ms	6123×	body	80	valid
67.0ms	699×	body	640	valid
44.0ms	351×	body	1280	valid
36.0ms	520×	body	320	valid
15.0ms	307×	body	160	valid