Details

sample20.0ms

Algorithm

intervals

Results

5.0ms	198×	body	80	valid
5.0ms	24×	body	640	valid
1.0ms	11×	body	1280	valid
1.0ms	15×	body	320	valid
0.0ms	8×	body	160	valid

simplify84.0ms

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: 13.9b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (+ y 1.0))
2.6b	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

rewrite8.0ms

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

series97.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ y (+ y 1.0))
61.0ms	(fma (/ y (+ y 1.0)) (- x 1.0) 1.0)

simplify114.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (108.0ms)

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

prune144.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ y 1.0))
0.1b	(* y (/ 1 (+ y 1.0)))
4.1b	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

rewrite20.0ms

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)

series122.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(/ 1 (+ y 1.0))
41.0ms	(* y (/ 1 (+ y 1.0)))
57.0ms	(fma (* y (/ 1 (+ y 1.0))) (- x 1.0) 1.0)

simplify51.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (43.0ms)

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

prune430.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ 1 (+ y 1.0)))
0.3b	(cbrt (/ 1 (+ y 1.0)))
0.3b	(cbrt (/ 1 (+ y 1.0)))
10.6b	(fma (* (* y (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0))))) (cbrt (/ 1 (+ y 1.0)))) (- x 1.0) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

54×	`cbrt-prod`
46×	`*-un-lft-identity`
36×	`times-frac`
28×	`add-sqr-sqrt` `add-cube-cbrt`
9×	`distribute-lft-out`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3-+` `pow1/3` `flip-+` `div-inv`
1×	`fma-udef`

Counts

4 → 97

Calls

4 calls:

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

series431.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (/ 1 (+ y 1.0)))
126.0ms	(cbrt (/ 1 (+ y 1.0)))
122.0ms	(cbrt (/ 1 (+ y 1.0)))
61.0ms	(fma (* (* y (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0))))) (cbrt (/ 1 (+ y 1.0)))) (- x 1.0) 1.0)

simplify109.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 3 (97.0ms)

Iter	Nodes	Cost
0	292	990
1	865	927
2	3257	859
3	5001	743

prune300.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ y 1.0))
0.3b	(cbrt (/ 1 (+ y 1.0)))
0.3b	(cbrt (/ 1 (+ y 1.0)))
9.7b	(fma (* (* y (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0))))) (/ 1 (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

40×	`cbrt-prod`
35×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `cbrt-div` `associate-/r/` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
2×	`div-inv`
1×	`fma-udef`

Counts

4 → 84

Calls

4 calls:

3.0ms	(cbrt (+ y 1.0))
8.0ms	(cbrt (/ 1 (+ y 1.0)))
5.0ms	(cbrt (/ 1 (+ y 1.0)))
1.0ms	(fma (* (* y (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0))))) (/ 1 (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

series402.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ y 1.0))
122.0ms	(cbrt (/ 1 (+ y 1.0)))
127.0ms	(cbrt (/ 1 (+ y 1.0)))
57.0ms	(fma (* (* y (* (cbrt (/ 1 (+ y 1.0))) (cbrt (/ 1 (+ y 1.0))))) (/ 1 (cbrt (+ y 1.0)))) (- x 1.0) 1.0)

simplify156.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	385	857
1	1182	801
2	4844	760
3	5001	760

prune329.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

regimes133.0ms

Accuracy

96.5% (0.2b remaining)

Error of 7.6b against oracle of 7.3b and baseline of 14.0b

bsearch119.0ms

Steps

Iters	Range		Point
8	1.2121919554764034e+30	4.2507803337288095e+32	7.875057675394472e+30
9	-7509027891406199.0	-1394632019.248084	-1041138812298367.4

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	28
1	50	28

end0.0ms

sample440.0ms

Algorithm

intervals

Results

155.0ms	6141×	body	80	valid
69.0ms	708×	body	640	valid
40.0ms	356×	body	1280	valid
33.0ms	483×	body	320	valid
14.0ms	312×	body	160	valid