Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	79×	body	1280	valid
6.0ms	52×	body	640	valid
2.0ms	104×	body	80	overflowed
2.0ms	25×	body	320	valid
2.0ms	88×	body	80	valid
1.0ms	12×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 42.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (exp x) (- (exp x) 1.0))
4.2b	(- (exp x) 1.0)

rewrite13.0ms

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:

6.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series42.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (exp x) (- (exp x) 1.0))
15.0ms	(- (exp x) 1.0)

simplify188.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (181.0ms)

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

prune128.0ms

Filtered

73 candidates to 50 candidates (68.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 0.0b

Counts

74 → 4

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)
1.0ms	(fma 1/12 x (/ 1 x))

series66.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(+ (fma 1/12 x (/ 1 x)) 1/2)
50.0ms	(fma 1/12 x (/ 1 x))

simplify39.0ms

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

prune60.0ms

Filtered

34 candidates to 26 candidates (76.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	1	34
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	33	5	38

Merged error: 0.0b

Counts

38 → 5

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)))
0.6b	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

rewrite11.0ms

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:

1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
1.0ms	(cbrt (fma 1/12 x (/ 1 x)))
6.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (fma 1/12 x (/ 1 x)))
106.0ms	(cbrt (fma 1/12 x (/ 1 x)))
105.0ms	(cbrt (fma 1/12 x (/ 1 x)))
122.0ms	(* (cbrt (fma 1/12 x (/ 1 x))) (cbrt (fma 1/12 x (/ 1 x))))

simplify135.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (119.0ms)

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

prune228.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	93	5	98

Merged error: 0.0b

Counts

98 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.0b	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
4.4b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
95×	`*-un-lft-identity`
63×	`add-sqr-sqrt` `add-cube-cbrt`
22×	`associate-/r*`
16×	`distribute-lft-out`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`add-exp-log`
6×	`div-inv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`fma-udef`

Counts

3 → 137

Calls

3 calls:

6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
10.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series207.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
86.0ms	(/ (exp x) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
48.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	490	2105
1	2157	2001
2	5001	1998

prune324.0ms

Filtered

146 candidates to 111 candidates (76.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	147	4	151

Merged error: 0.0b

Counts

151 → 4

regimes27.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.6b against oracle of 0.3b and baseline of 21.5b

bsearch49.0ms

Steps

Iters	Range		Point
10	-0.05202343663643454	-5.738045557766166e-18	-0.0014783118370881984

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	21
1	35	21

end0.0ms

sample1.1s

Algorithm

intervals

Results

403.0ms	2202×	body	1280	valid
345.0ms	1663×	body	640	valid
64.0ms	828×	body	320	valid
62.0ms	2869×	body	80	valid
51.0ms	2510×	body	80	overflowed
26.0ms	439×	body	160	valid