Details

sample90.0ms

Algorithm

intervals

Results

36.0ms	94×	body	1280	valid
20.0ms	80×	body	640	valid
11.0ms	222×	body	80	overflowed
10.0ms	47×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	18×	body	80	valid

simplify45.0ms

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: 0.5b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(expm1 (+ x x))
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

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

series112.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(expm1 (+ x x))
21.0ms	(fma 1 1 (exp (+ x x)))
72.0ms	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify80.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (74.0ms)

Iter	Nodes	Cost
0	164	440
1	564	391
2	2669	384
3	5001	382

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* 2 x)) 1)
0.0b	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
0.0b	(pow (+ (exp (* 2 x)) 1) 3)
0.5b	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
7×	`add-exp-log`
6×	`cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `expm1-udef` `rem-cube-cbrt`

Counts

4 → 161

Calls

4 calls:

4.0ms	(+ (exp (* 2 x)) 1)
9.0ms	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
6.0ms	(pow (+ (exp (* 2 x)) 1) 3)
16.0ms	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))

series109.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (exp (* 2 x)) 1)
10.0ms	(cbrt (pow (+ (exp (* 2 x)) 1) 3))
36.0ms	(pow (+ (exp (* 2 x)) 1) 3)
52.0ms	(/ (expm1 (+ x x)) (cbrt (pow (+ (exp (* 2 x)) 1) 3)))

simplify65.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	378	1647
1	1691	1481
2	5001	1423

prune314.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (+ x x))
0.0b	(+ (exp (* 2 x)) 1)
0.0b	(/ 1 (+ (exp (* 2 x)) 1))
0.5b	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

40×	`*-un-lft-identity`
30×	`add-sqr-sqrt`
26×	`times-frac`
23×	`add-cube-cbrt`
18×	`associate-r`
17×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`distribute-lft-out`
7×	`pow1`
6×	`add-log-exp`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `associate-/r*` `associate-/r/`
3×	`fma-def` `flip3-+` `associate-l` `flip-+` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `1-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `expm1-log1p` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

1.0ms	(expm1 (+ x x))
4.0ms	(+ (exp (* 2 x)) 1)
7.0ms	(/ 1 (+ (exp (* 2 x)) 1))
19.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series110.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(expm1 (+ x x))
10.0ms	(+ (exp (* 2 x)) 1)
19.0ms	(/ 1 (+ (exp (* 2 x)) 1))
57.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify47.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	816
1	1707	645
2	5001	631

prune222.0ms

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)))
0.1b	(* 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))

series176.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
82.0ms	(- x (* 1/3 (pow x 3)))
42.0ms	(* 1/3 (pow x 3))

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (31.0ms)

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

prune156.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

regimes15.0ms

Accuracy

0% (0.2b remaining)

Error of 0.8b against oracle of 0.6b and baseline of 0.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	20	8
2	20	8

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3379×	body	1280	valid
610.0ms	2417×	body	640	valid
360.0ms	7577×	body	80	overflowed
199.0ms	1219×	body	320	valid
63.0ms	589×	body	160	valid
21.0ms	396×	body	80	valid