Details

sample74.0ms

Algorithm

intervals

Results

33.0ms	101×	body	1280	valid
15.0ms	82×	body	640	valid
8.0ms	268×	body	80	overflowed
5.0ms	39×	body	320	valid
2.0ms	24×	body	160	valid
0.0ms	10×	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

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 3 expressions with local error:

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

series104.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(fma 1 1 (exp (+ x x)))
18.0ms	(expm1 (+ x x))
67.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify78.0ms

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

prune148.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.0b	(expm1 (+ x x))
0.0b	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
0.1b	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
16×	`associate-/r*`
11×	`add-cbrt-cube`
8×	`div-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1` `log1p-expm1-u`
4×	`cbrt-undiv` `expm1-log1p-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`expm1-log1p` `pow-flip` `associate-/r/` `fma-udef` `inv-pow` `expm1-udef`

Counts

4 → 128

Calls

4 calls:

0.0ms	(fma 1 1 (exp (+ x x)))
0.0ms	(expm1 (+ x x))
2.0ms	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
5.0ms	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

series170.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(fma 1 1 (exp (+ x x)))
17.0ms	(expm1 (+ x x))
67.0ms	(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
66.0ms	(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	401	1494
1	1795	1297
2	5002	1209

prune249.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* 2 x)) 1)
0.0b	(/ 1 (+ (exp (* 2 x)) 1))
0.0b	(/ 1 (expm1 (+ x x)))
0.2b	(/ (/ 1 (+ (exp (* 2 x)) 1)) (/ 1 (expm1 (+ x x))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

594×	`times-frac`
361×	`*-un-lft-identity`
267×	`add-sqr-sqrt` `add-cube-cbrt`
52×	`add-exp-log`
47×	`distribute-lft-out`
36×	`div-exp` `div-inv`
31×	`associate-/r/`
24×	`associate-/l*`
20×	`associate-/r*` `add-cbrt-cube`
16×	`flip3-+` `flip-+`
10×	`cbrt-undiv` `rec-exp` `1-exp`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`+-commutative` `sum-log` `associate-/l/`

Counts

4 → 388

Calls

4 calls:

4.0ms	(+ (exp (* 2 x)) 1)
7.0ms	(/ 1 (+ (exp (* 2 x)) 1))
2.0ms	(/ 1 (expm1 (+ x x)))
23.0ms	(/ (/ 1 (+ (exp (* 2 x)) 1)) (/ 1 (expm1 (+ x x))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (exp (* 2 x)) 1)
18.0ms	(/ 1 (+ (exp (* 2 x)) 1))
25.0ms	(/ 1 (expm1 (+ x x)))
56.0ms	(/ (/ 1 (+ (exp (* 2 x)) 1)) (/ 1 (expm1 (+ x x))))

simplify77.0ms

Algorithm

egg-herbie

Counts

400 → 400

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1467	5893
1	5001	4758

prune389.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

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)))
0.1b	(* 1/3 (pow x 3))

rewrite12.0ms

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))))
3.0ms	(- x (* 1/3 (pow x 3)))
7.0ms	(* 1/3 (pow x 3))

series168.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
78.0ms	(- x (* 1/3 (pow x 3)))
35.0ms	(* 1/3 (pow x 3))

simplify35.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	206	343
1	832	296
2	5002	295

prune157.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes11.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.5b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	8
1	19	8
2	19	8

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.0s	3275×	body	1280	valid
479.0ms	2514×	body	640	valid
212.0ms	7564×	body	80	overflowed
140.0ms	1179×	body	320	valid
47.0ms	616×	body	160	valid
16.0ms	416×	body	80	valid