Details

sample109.0ms

Algorithm

intervals

Results

45.0ms	270×	body	10240	exit
33.0ms	110×	body	1280	valid
12.0ms	67×	body	640	valid
4.0ms	42×	body	320	valid
1.0ms	20×	body	160	valid
1.0ms	17×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 1 1 (exp (+ x x)))
0.7b	(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite7.0ms

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

series96.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(fma 1 1 (exp (+ x x)))
74.0ms	(/ (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

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.7b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (+ (exp (* 2 x)) 1))
0.0b	(+ (exp (* 2 x)) 1)
0.7b	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 99

Calls

3 calls:

20.0ms	(/ 1 (+ (exp (* 2 x)) 1))
11.0ms	(+ (exp (* 2 x)) 1)
41.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series89.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(/ 1 (+ (exp (* 2 x)) 1))
11.0ms	(+ (exp (* 2 x)) 1)
53.0ms	(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify43.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	320	771
1	1601	634
2	5001	594

prune210.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 2 expressions with local error:

0.7b	(* (expm1 (+ x x)) (exp (- 0 (log1p (exp (* 2 x))))))
0.7b	(log1p (exp (* 2 x)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

14×	`associate-r`
12×	`add-sqr-sqrt`
11×	`exp-sum`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`prod-diff`
4×	`pow1` `add-cbrt-cube`
3×	`add-exp-log` `expm1-log1p-u` `associate-l`
2×	`exp-neg` `sub0-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
1×	`sub-neg` `log1p-udef` `exp-diff` `log1p-expm1` `pow-prod-down` `prod-exp` `un-div-inv` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 45

Calls

2 calls:

58.0ms	(* (expm1 (+ x x)) (exp (- 0 (log1p (exp (* 2 x))))))
1.0ms	(log1p (exp (* 2 x)))

series326.0ms

Counts

2 → 6

Calls

2 calls:

274.0ms	(* (expm1 (+ x x)) (exp (- 0 (log1p (exp (* 2 x))))))
52.0ms	(log1p (exp (* 2 x)))

simplify134.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	233	461
1	898	359
2	4624	329
3	5001	329

prune133.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
8×	`add-exp-log`
7×	`associate-l`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`add-cbrt-cube`
4×	`unpow-prod-down`
3×	`pow1` `expm1-log1p-u` `associate-r` `prod-exp` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`fma-udef` `sqr-pow`
1×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod`

Counts

3 → 47

Calls

3 calls:

0.0ms	(fma 1 x (* (pow x 5) 2/15))
0.0ms	(fma 1/3 (- (pow x 3)) (fma 1 x (* (pow x 5) 2/15)))
12.0ms	(* (pow x 5) 2/15)

series229.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(fma 1 x (* (pow x 5) 2/15))
62.0ms	(fma 1/3 (- (pow x 3)) (fma 1 x (* (pow x 5) 2/15)))
49.0ms	(* (pow x 5) 2/15)

simplify75.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	143	265
1	510	235
2	2311	230
3	5003	229

prune154.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

regimes16.0ms

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	18	8
1	20	8
2	20	8

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.3s	7689×	body	10240	exit
1.0s	3349×	body	1280	valid
439.0ms	2470×	body	640	valid
126.0ms	1173×	body	320	valid
39.0ms	592×	body	160	valid
15.0ms	416×	body	80	valid