Details

sample102.0ms

Algorithm

intervals

Results

41.0ms	234×	body	10240	exit
31.0ms	101×	body	1280	valid
15.0ms	87×	body	640	valid
4.0ms	39×	body	320	valid
1.0ms	18×	body	160	valid
0.0ms	11×	body	80	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (44.0ms)

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

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

series89.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	150	395
1	512	351
2	2464	344
3	5002	343

prune117.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0b	(- x (* 1/3 (pow x 3)))
0.2b	(* 1/3 (pow x 3))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
12×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-diff` `prod-exp` `log1p-expm1-u`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `fma-udef`

Counts

3 → 63

Calls

3 calls:

0.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
2.0ms	(- x (* 1/3 (pow x 3)))
7.0ms	(* 1/3 (pow x 3))

series170.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
79.0ms	(- x (* 1/3 (pow x 3)))
36.0ms	(* 1/3 (pow x 3))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5002	292

prune161.0ms

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	(- x (* 1/3 (pow x 3)))
0.1b	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.2b	(* 1/3 (pow x 3))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `unpow-prod-down` `cube-prod` `log1p-expm1-u` `unswap-sqr`
3×	`fma-neg` `associate-l` `prod-diff` `prod-exp`
2×	`sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `unpow3` `log1p-expm1` `pow-exp` `*-commutative` `flip--` `cbrt-unprod` `expm1-udef`

Counts

4 → 75

Calls

4 calls:

0.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
5.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
7.0ms	(* 1/3 (pow x 3))

series366.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
79.0ms	(- x (* 1/3 (pow x 3)))
156.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
36.0ms	(* 1/3 (pow x 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	354	521
1	1434	454
2	5001	432

prune246.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(- x (* 1/3 (pow x 3)))
0.0b	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
0.1b	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
0.2b	(* 1/3 (pow x 3))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
12×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`fma-neg` `associate-l` `prod-diff` `prod-exp`
2×	`expm1-log1p` `expm1-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 75

Calls

4 calls:

2.0ms	(- x (* 1/3 (pow x 3)))
0.0ms	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
0.0ms	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
7.0ms	(* 1/3 (pow x 3))

series555.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- x (* 1/3 (pow x 3)))
182.0ms	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
257.0ms	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
35.0ms	(* 1/3 (pow x 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	355	571
1	1413	488
2	5001	464

prune263.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

regimes24.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	6
1	13	6
2	13	6

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	7781×	body	10240	exit
1.0s	3383×	body	1280	valid
427.0ms	2383×	body	640	valid
134.0ms	1207×	body	320	valid
43.0ms	606×	body	160	valid
15.0ms	421×	body	80	valid