Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	193×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	20×	body	320	valid
1.0ms	10×	body	1280	valid
0.0ms	11×	body	160	valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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: 14.7b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.8b	(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))
1.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series95.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify112.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (107.0ms)

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

prune146.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ y 1.0))
0.1b	(* y (/ 1 (+ y 1.0)))
5.4b	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

5.0ms	(/ 1 (+ y 1.0))
10.0ms	(* y (/ 1 (+ y 1.0)))
1.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

series119.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/ 1 (+ y 1.0))
35.0ms	(* y (/ 1 (+ y 1.0)))
60.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	324	499
1	1447	427
2	5002	381

prune215.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

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

rewrite11.0ms

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)))) (/ 1 (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series354.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (+ y 1.0))
97.0ms	(cbrt (+ y 1.0))
99.0ms	(cbrt (+ y 1.0))
61.0ms	(fma (* (/ y (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ 1 (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify83.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	235	565
1	698	515
2	2650	500
3	5001	468

prune282.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
11.0b	(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)

series656.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(cbrt y)
189.0ms	(cbrt y)
190.0ms	(cbrt y)
77.0ms	(fma (/ (* (cbrt y) (cbrt y)) (/ (+ y 1.0) (cbrt y))) (- x 1.0) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (37.0ms)

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

prune188.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.6b

regimes127.0ms

Accuracy

96.2% (0.3b remaining)

Error of 7.5b against oracle of 7.2b and baseline of 14.2b

bsearch108.0ms

Steps

Iters	Range		Point
10	2.7767344490878063e+53	3.608477260869243e+64	1.1941330995112353e+55
9	-7.755278215516031e+26	-5.651135004763443e+21	-5.729793113088247e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	9
1	26	9

end0.0ms

sample460.0ms

Algorithm

intervals

Results

158.0ms	6115×	body	80	valid
66.0ms	738×	body	640	valid
46.0ms	367×	body	1280	valid
38.0ms	496×	body	320	valid
13.0ms	284×	body	160	valid