Details

sample20.0ms

Algorithm

intervals

Results

6.0ms	200×	body	80	valid
3.0ms	27×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	10×	body	160	valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (16.0ms)

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

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
3.2b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite13.0ms

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:

11.0ms	(/ y (+ y 1.0))
0.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

series92.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ y (+ y 1.0))
53.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify124.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (119.0ms)

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

prune201.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.2b

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)

rewrite49.0ms

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:

12.0ms	(/ 1 (+ y 1.0))
34.0ms	(* y (/ 1 (+ y 1.0)))
0.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

series112.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(/ 1 (+ y 1.0))
39.0ms	(* y (/ 1 (+ y 1.0)))
52.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (47.0ms)

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

prune292.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.2b

localize13.0ms

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)) (cbrt (+ y 1.0)))
9.7b	(fma (* y (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ 1 (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

rewrite52.0ms

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:

4.0ms	(cbrt (+ y 1.0))
4.0ms	(cbrt (+ y 1.0))
41.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
0.0ms	(fma (* y (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ 1 (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

series340.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt (+ y 1.0))
93.0ms	(cbrt (+ y 1.0))
113.0ms	(* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))
51.0ms	(fma (* y (* (/ 1 (* (cbrt (+ y 1.0)) (cbrt (+ y 1.0)))) (/ 1 (cbrt (+ y 1.0))))) (- x 1.0) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	373	892
1	1305	824
2	5002	762

prune624.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
0.6b	(cbrt y)
9.2b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

rewrite4.0ms

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

series656.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(cbrt y)
191.0ms	(cbrt y)
192.0ms	(cbrt y)
72.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (+ y 1.0))) (- x 1.0) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	104	277
1	282	243
2	1092	232
3	5002	228

prune299.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.2b

regimes499.0ms

Accuracy

97% (0.2b remaining)

Error of 7.3b against oracle of 7.0b and baseline of 14.6b

bsearch96.0ms

Steps

Iters	Range		Point
9	3202614516610.6147	3.177175472717041e+17	26612025094197484.0
8	-2.0299508383700634e+24	-3.618275887393801e+21	-3.660457764379565e+21

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	9
1	23	9

end0.0ms

sample512.0ms

Algorithm

intervals

Results

183.0ms	6130×	body	80	valid
77.0ms	728×	body	640	valid
48.0ms	344×	body	1280	valid
42.0ms	499×	body	320	valid
16.0ms	299×	body	160	valid