Details

sample37.0ms

Algorithm

intervals

Results

11.0ms	63×	body	1280	valid
9.0ms	65×	body	10240	exit
5.0ms	46×	body	640	valid
2.0ms	109×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	14×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	4
1	8	4
2	8	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
3.9b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`times-frac`
9×	`prod-diff`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-neg` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 67

Calls

2 calls:

8.0ms	(/ (exp x) (- (exp x) 1.0))
5.0ms	(- (exp x) 1.0)

series40.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(/ (exp x) (- (exp x) 1.0))
14.0ms	(- (exp x) 1.0)

simplify185.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (179.0ms)

Iter	Nodes	Cost
0	237	520
1	786	429
2	4651	416
3	5001	404

prune143.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b	(fma 1/12 x (/ 1 x))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`*-un-lft-identity`
4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

2 → 28

Calls

2 calls:

3.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms	(fma 1/12 x (/ 1 x))

series62.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
47.0ms	(fma 1/12 x (/ 1 x))

simplify37.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	90	126
1	306	119
2	1283	117
3	5001	116

prune65.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
0.5b	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

2.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
2.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
2.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
21.0ms	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
75.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
68.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
58.0ms	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))

simplify48.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	330	1259
1	1115	1189
2	5001	1083

prune279.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
0.3b	(/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x))))
3.8b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube`
9×	`add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `associate-/r` `flip-+` `associate-/l`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `fma-udef`

Counts

4 → 97

Calls

4 calls:

21.0ms	(* (/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0))
4.0ms	(+ (exp x) 1.0)
3.0ms	(/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x))))
0.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
78.0ms	(/ (exp x) (fma (- 1.0) 1.0 (exp (+ x x))))
47.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	436	984
1	1853	887
2	5002	871

prune273.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes66.0ms

Accuracy

98.2% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 21.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	13
1	21	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

378.0ms	2189×	body	1280	valid
280.0ms	2544×	body	10240	exit
173.0ms	1600×	body	640	valid
62.0ms	843×	body	320	valid
62.0ms	2949×	body	80	valid
19.0ms	421×	body	160	valid