Details

sample100.0ms

Algorithm

intervals

Results

38.0ms	225×	body	10240	exit
32.0ms	108×	body	1280	valid
16.0ms	88×	body	640	valid
4.0ms	34×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	14×	body	80	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 7 (43.0ms)

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: 0.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.3b	(/ (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))))

series94.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 1 1 (exp (+ x x)))
72.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune113.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize12.0ms

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))))
7.0ms	(* 1/3 (pow x 3))

series95.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
38.0ms	(* 1/3 (pow x 3))

simplify166.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (6.0ms)

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

prune109.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

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

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

series346.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
94.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
156.0ms	(expm1 (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))
40.0ms	(* 1/3 (pow x 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (34.0ms)

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

prune213.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

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

series581.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))))
98.0ms	(log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3)))))
254.0ms	(expm1 (expm1 (log1p (log1p (fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))))))
38.0ms	(* 1/3 (pow x 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	309	537
1	1197	464
2	5002	441

prune265.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

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

sample3.1s

Algorithm

intervals

Results

1.3s	7578×	body	10240	exit
990.0ms	3355×	body	1280	valid
434.0ms	2444×	body	640	valid
126.0ms	1161×	body	320	valid
41.0ms	617×	body	160	valid
15.0ms	423×	body	80	valid