Details

sample102.0ms

Algorithm

intervals

Results

41.0ms	247×	body	10240	exit
31.0ms	103×	body	1280	valid
13.0ms	74×	body	640	valid
5.0ms	45×	body	320	valid
1.0ms	19×	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: 0.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.8b	(/ (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))))

series88.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
68.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify73.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (68.0ms)

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

prune126.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 3 expressions with local error:

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

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

series170.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify38.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	206	338
1	835	292
2	5001	292

prune171.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

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

rewrite12.0ms

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))))))
10.0ms	(* 1/3 (pow x 3))

series342.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
56.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
155.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
35.0ms	(* 1/3 (pow x 3))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

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

prune230.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
0.0b	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
0.0b	(expm1 (expm1 (log1p (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` `log1p-expm1-u`
4×	`pow1` `unpow-prod-down` `cube-prod` `add-log-exp` `unswap-sqr`
3×	`associate-l` `prod-exp`
2×	`expm1-log1p` `expm1-udef` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `log1p-udef` `unpow3` `log1p-expm1` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 66

Calls

4 calls:

0.0ms	(log1p (log1p (fma (pow x 5) 2/15 (- 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))

series621.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
187.0ms	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
252.0ms	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
40.0ms	(* 1/3 (pow x 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	414	629
1	1800	547
2	5002	539

prune259.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes56.0ms

Accuracy

0% (1.4b remaining)

Error of 2.0b against oracle of 0.6b and baseline of 2.0b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	22	9
2	22	9

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.3s	7626×	body	10240	exit
984.0ms	3276×	body	1280	valid
439.0ms	2388×	body	640	valid
138.0ms	1247×	body	320	valid
45.0ms	636×	body	160	valid
16.0ms	453×	body	80	valid