Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	199×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	9×	body	1280	valid
1.0ms	15×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (10.0ms)

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.8b	(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))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series93.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ y (+ y 1.0))
58.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify105.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (100.0ms)

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

prune135.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.0b

localize11.0ms

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))
10.8b	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite8.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
0.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series340.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ y 1.0))
94.0ms	(cbrt (+ y 1.0))
94.0ms	(cbrt (+ y 1.0))
60.0ms	(fma (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ y (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify75.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	235	565
1	699	515
2	2697	493
3	5001	461

prune255.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize20.0ms

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))
10.8b	(fma (* (/ 1 (* (* (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)

rewrite8.0ms

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:

2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
2.0ms	(cbrt (+ y 1.0))
0.0ms	(fma (* (/ 1 (* (* (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)

series328.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ y 1.0))
92.0ms	(cbrt (+ y 1.0))
91.0ms	(cbrt (+ y 1.0))
54.0ms	(fma (* (/ 1 (* (* (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)

simplify94.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	241	669
1	727	603
2	2997	588
3	5001	559

prune317.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
3.8b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.8b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
3.8b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series283.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (fma (/ y (+ y 1.0)) (- x 1.0) 1.0))
59.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
54.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)
58.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	168	405
1	501	355
2	1834	340
3	5002	325

prune184.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.9b

regimes101.0ms

Accuracy

94.7% (0.4b remaining)

Error of 7.6b against oracle of 7.2b and baseline of 15.0b

bsearch80.0ms

Steps

Iters	Range		Point
9	2.5213731220351086e+91	7.970210972913177e+99	2.5663705514386888e+91
5	-3.5449486289448466e+25	-1.324502305282769e+25	-1.3466134406715405e+25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	16
1	33	16

end0.0ms

sample431.0ms

Algorithm

intervals

Results

149.0ms	6092×	body	80	valid
70.0ms	748×	body	640	valid
36.0ms	333×	body	1280	valid
35.0ms	539×	body	320	valid
13.0ms	288×	body	160	valid