Details

sample38.0ms

Algorithm

intervals

Results

13.0ms	78×	body	1280	valid
7.0ms	69×	body	10240	exit
6.0ms	56×	body	640	valid
2.0ms	25×	body	320	valid
2.0ms	88×	body	80	valid
0.0ms	9×	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: 42.7b

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
2.7b	(- (exp x) 1.0)

rewrite15.0ms

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)

series44.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify189.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (183.0ms)

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

prune143.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

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))

series58.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
43.0ms	(fma 1/12 x (/ 1 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (35.0ms)

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

prune65.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

0.0ms	(cbrt (fma 1/12 x (/ 1 x)))
0.0ms	(cbrt (fma 1/12 x (/ 1 x)))
0.0ms	(cbrt (fma 1/12 x (/ 1 x)))
6.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (fma 1/12 x (/ 1 x)))
97.0ms	(cbrt (fma 1/12 x (/ 1 x)))
100.0ms	(cbrt (fma 1/12 x (/ 1 x)))
108.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

simplify129.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	277	823
1	917	765
2	4127	688
3	5002	652

prune242.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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:

22.0ms	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (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))
2.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))

series263.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)) (cbrt (+ (fma 1/12 x (/ 1 x)) 1/2)))
72.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
65.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))
72.0ms	(cbrt (+ (fma 1/12 x (/ 1 x)) 1/2))

simplify47.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	330	1284
1	1109	1214
2	5001	1108

prune262.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes45.0ms

Accuracy

96.1% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 21.1b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample1.1s

Algorithm

intervals

Results

390.0ms	2327×	body	1280	valid
268.0ms	2534×	body	10240	exit
171.0ms	1635×	body	640	valid
54.0ms	807×	body	320	valid
53.0ms	2835×	body	80	valid
17.0ms	397×	body	160	valid