Details

sample34.0ms

Algorithm

intervals

Results

12.0ms	185×	body	80	valid
6.0ms	29×	body	640	valid
3.0ms	12×	body	1280	valid
3.0ms	20×	body	320	valid
1.0ms	10×	body	160	valid

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (14.0ms)

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: 16.6b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.4b	(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:

6.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series100.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ y (+ y 1.0))
64.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify117.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (111.0ms)

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

prune153.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.4b	(fma (* 1 (/ 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 (* 1 (/ y (+ y 1.0))) (- x 1.0) 1.0)

series101.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(/ y (+ y 1.0))
58.0ms	(fma (* 1 (/ y (+ y 1.0))) (- x 1.0) 1.0)

simplify144.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (139.0ms)

Iter	Nodes	Cost
0	207	275
1	793	247
2	3841	241
3	5001	237

prune144.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
2.4b	(fma (* 1 (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt y) (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

rewrite3.0ms

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

series677.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt y)
196.0ms	(cbrt y)
204.0ms	(cbrt y)
78.0ms	(fma (* 1 (* (/ (* (cbrt y) (cbrt y)) (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ (cbrt y) (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

simplify67.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	117	380
1	375	324
2	2211	306
3	5002	293

prune249.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.4b

localize12.0ms

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))
13.1b	(fma (* 1 (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (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 (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series365.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (+ y 1.0))
100.0ms	(cbrt (+ y 1.0))
100.0ms	(cbrt (+ y 1.0))
64.0ms	(fma (* 1 (/ (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify85.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	234	564
1	696	509
2	2698	485
3	5001	450

prune256.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.3b

regimes133.0ms

Accuracy

96.8% (0.2b remaining)

Error of 7.6b against oracle of 7.3b and baseline of 14.2b

bsearch110.0ms

Steps

Iters	Range		Point
10	1.8947657802636736e+39	1.291035463734514e+53	2.535884636422971e+46
6	-4.686375692591297e+43	-3.384922884554694e+42	-3.468473154262352e+42

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	13
1	32	13
2	32	13

end0.0ms

sample809.0ms

Algorithm

intervals

Results

324.0ms	6115×	body	80	valid
148.0ms	734×	body	640	valid
88.0ms	368×	body	1280	valid
74.0ms	507×	body	320	valid
26.0ms	276×	body	160	valid