Details

sample89.0ms

Algorithm

intervals

Results

39.0ms	99×	body	1280	valid
19.0ms	75×	body	640	valid
11.0ms	218×	body	80	overflowed
8.0ms	45×	body	320	valid
2.0ms	21×	body	160	valid
1.0ms	16×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

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

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:

26.0ms	(fma 1 1 (exp (+ x x)))
63.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify76.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

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

prune114.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(exp (log1p (exp (* 2 x))))
0.5b	(log1p (exp (* 2 x)))
0.5b	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

1.0ms	(exp (log1p (exp (* 2 x))))
0.0ms	(log1p (exp (* 2 x)))
3.0ms	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

series269.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(exp (log1p (exp (* 2 x))))
50.0ms	(log1p (exp (* 2 x)))
140.0ms	(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	182	523
1	556	477
2	2509	465
3	5001	451

prune161.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1 (exp x))
0.8b	(/ (expm1 (* 2 x)) (hypot 1 (exp x)))
0.9b	(* (/ 1 (/ (hypot 1 (exp x)) 1)) (/ (expm1 (* 2 x)) (hypot 1 (exp x))))
0.9b	(/ 1 (/ (hypot 1 (exp x)) 1))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
141×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
96×	`add-cube-cbrt`
83×	`add-exp-log`
47×	`div-exp`
44×	`associate-l`
32×	`add-cbrt-cube`
20×	`prod-exp`
18×	`1-exp`
16×	`associate-/r*`
14×	`unswap-sqr`
13×	`cbrt-undiv` `associate-r`
11×	`div-inv`
9×	`rec-exp`
7×	`pow1`
6×	`cbrt-unprod` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`frac-times` `hypot-udef` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow` `expm1-udef`

Counts

4 → 232

Calls

4 calls:

0.0ms	(hypot 1 (exp x))
2.0ms	(/ (expm1 (* 2 x)) (hypot 1 (exp x)))
31.0ms	(* (/ 1 (/ (hypot 1 (exp x)) 1)) (/ (expm1 (* 2 x)) (hypot 1 (exp x))))
5.0ms	(/ 1 (/ (hypot 1 (exp x)) 1))

series416.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(hypot 1 (exp x))
120.0ms	(/ (expm1 (* 2 x)) (hypot 1 (exp x)))
153.0ms	(* (/ 1 (/ (hypot 1 (exp x)) 1)) (/ (expm1 (* 2 x)) (hypot 1 (exp x))))
86.0ms	(/ 1 (/ (hypot 1 (exp x)) 1))

simplify46.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1001	2593
1	5001	2228

prune486.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

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))

series174.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
80.0ms	(- x (* 1/3 (pow x 3)))
37.0ms	(* 1/3 (pow x 3))

simplify36.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (7.0ms)

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

prune159.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.5b

regimes21.0ms

Accuracy

0% (0.1b remaining)

Error of 0.8b against oracle of 0.7b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	17	7
2	17	7

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3316×	body	1280	valid
621.0ms	2462×	body	640	valid
373.0ms	7563×	body	80	overflowed
204.0ms	1216×	body	320	valid
66.0ms	593×	body	160	valid
22.0ms	413×	body	80	valid