Details

sample97.0ms

Algorithm

intervals

Results

44.0ms	107×	body	1280	valid
18.0ms	74×	body	640	valid
15.0ms	223×	body	80	overflowed
5.0ms	28×	body	320	valid
4.0ms	32×	body	160	valid
1.0ms	15×	body	80	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (45.0ms)

Iter	Nodes	Cost
0	15	9
1	24	9
2	32	9
3	44	9
4	63	9
5	179	9
6	1184	9
7	5001	7

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(fma 1 1 (exp (+ x x)))
0.5b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube`
4×	`log1p-expm1-u`
3×	`pow1` `expm1-log1p-u` `associate-/r` `associate-/l` `add-log-exp`
2×	`expm1-udef`
1×	`cbrt-undiv` `expm1-log1p` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

3 → 51

Calls

3 calls:

0.0ms	(expm1 (+ x x))
0.0ms	(fma 1 1 (exp (+ x x)))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series107.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(expm1 (+ x x))
21.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify79.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	164	440
1	564	391
2	2669	384
3	5001	382

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.0b	(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
0.5b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`expm1-udef`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `div-sub` `log1p-expm1` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 62

Calls

4 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
0.0ms	(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
0.0ms	(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
2.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series353.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma 1 1 (exp (+ x x)))
178.0ms	(log1p (expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))))
83.0ms	(expm1 (/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x)))))
67.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify87.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	190	626
1	623	553
2	2844	544
3	5002	542

prune192.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b	(* 1/3 (pow x 3))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`associate-r`
7×	`add-exp-log`
6×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `add-cbrt-cube` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

2 → 43

Calls

2 calls:

0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
6.0ms	(* 1/3 (pow x 3))

series93.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
39.0ms	(* 1/3 (pow x 3))

simplify167.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	149	210
1	589	185
2	3445	185
3	5001	185

prune110.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.1b	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.1b	(* 1/3 (pow x 3))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-exp-log`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-cbrt-cube`
5×	`expm1-log1p-u`
4×	`pow1` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `log1p-udef` `expm1-log1p` `unpow3` `log1p-expm1` `pow-exp` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef`

Counts

4 → 65

Calls

4 calls:

0.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
6.0ms	(* 1/3 (pow x 3))

series332.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
145.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
40.0ms	(* 1/3 (pow x 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	306	465
1	1191	409
2	5001	389

prune208.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

regimes19.0ms

Accuracy

0% (0.1b remaining)

Error of 0.6b against oracle of 0.5b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	8
1	15	8
2	15	8

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.3s	3324×	body	1280	valid
606.0ms	2414×	body	640	valid
459.0ms	7291×	body	80	overflowed
210.0ms	1223×	body	320	valid
75.0ms	625×	body	160	valid
31.0ms	414×	body	80	valid