Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	187×	body	80	valid
2.0ms	23×	body	640	valid
2.0ms	30×	body	320	valid
1.0ms	9×	body	1280	valid
0.0ms	7×	body	160	valid

simplify70.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (9.0ms)

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

prune8.0ms

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: 16.3b

Counts

2 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite7.0ms

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:

5.0ms	(/ y (+ y 1.0))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series90.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ y (+ y 1.0))
52.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify104.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	203	263
1	708	238
2	3148	232
3	5002	228

prune119.0ms

Filtered

51 candidates to 40 candidates (78.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	43	8	51
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 9.8b

Counts

53 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ y 1.0))
0.2b	(cbrt (+ y 1.0))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
12.3b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 97

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
3.0ms	(cbrt (+ y 1.0))
10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
1.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series343.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (+ y 1.0))
91.0ms	(cbrt (+ y 1.0))
104.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
58.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	370	879
1	1298	813
2	5001	756

prune286.0ms

Filtered

109 candidates to 79 candidates (72.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	5	109
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	108	10	118

Merged error: 9.8b

Counts

118 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.3b	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
12.0b	(fma (* (/ 1 (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

72×	`cbrt-prod`
70×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
36×	`cbrt-div`
28×	`add-cube-cbrt`
27×	`swap-sqr`
25×	`pow1`
21×	`associate-r` `associate-l`
18×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
12×	`frac-times` `unswap-sqr`
10×	`add-exp-log`
6×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 175

Calls

4 calls:

10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
10.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
1.0ms	(fma (* (/ 1 (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series370.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
109.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
103.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
57.0ms	(fma (* (/ 1 (* (* (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0))))) (cbrt (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	284	1702
1	1005	1561
2	5002	1408

prune485.0ms

Filtered

187 candidates to 117 candidates (62.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	186	1	187
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	187	10	197

Merged error: 9.8b

Counts

197 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
12.5b	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 49

Calls

4 calls:

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

series603.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt y)
176.0ms	(cbrt y)
181.0ms	(cbrt y)
66.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	104	277
1	278	244
2	1012	231
3	5002	227

prune140.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	59	2	61
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	59	12	71

Merged error: 9.8b

Counts

71 → 12

regimes103.0ms

Accuracy

97.6% (0.2b remaining)

Error of 7.4b against oracle of 7.2b and baseline of 14.8b

bsearch64.0ms

Steps

Iters	Range		Point
11	8.601567399579238	1.5547008822323828e+25	1.832781232452173e+16
3	-5.2457745834137905e+31	-3.8757153595728125e+31	-3.924178665354016e+31

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	8
1	21	8

end0.0ms

sample520.0ms

Algorithm

intervals

Results

193.0ms	6034×	body	80	valid
80.0ms	749×	body	640	valid
49.0ms	358×	body	1280	valid
48.0ms	587×	body	320	valid
15.0ms	272×	body	160	valid