Details

sample28.0ms

Algorithm

intervals

Results

11.0ms	72×	body	1280	valid
4.0ms	43×	body	640	valid
3.0ms	177×	body	80	valid
2.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	3
1	13	3
2	15	3
3	15	3

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: 37.7b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
3.9b	(- (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-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`fma-neg` `associate-/r*`
2×	`pow1` `expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

2 → 68

Calls

2 calls:

7.0ms	(/ (- (exp x) 1.0) x)
4.0ms	(- (exp x) 1.0)

series59.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- (exp x) 1.0) x)
15.0ms	(- (exp x) 1.0)

simplify34.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	282	468
1	919	380
2	5001	377

prune113.0ms

Filtered

74 candidates to 52 candidates (70.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	71	3	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	3	75

Merged error: 0.0b

Counts

75 → 3

localize6.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 1/6 (pow x 2) (fma 1/2 x 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(fma 1/6 (pow x 2) (fma 1/2 x 1))

simplify24.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	36	59
1	104	52
2	535	52
3	5002	52

prune26.0ms

Filtered

13 candidates to 10 candidates (76.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	13	3	16

Merged error: 0.0b

Counts

16 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`add-cube-cbrt`
30×	`log-pow`
27×	`times-frac`
25×	`exp-prod`
18×	`prod-diff`
14×	`log-prod`
11×	`exp-sum`
9×	`associate-/l*`
8×	`pow1`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `fma-neg` `associate-/r*` `log1p-expm1-u`
2×	`sub-neg` `log-div` `exp-diff`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `diff-log` `div-sub` `div-exp` `rem-log-exp` `clear-num` `flip--` `div-inv`

Counts

3 → 113

Calls

3 calls:

9.0ms	(/ (log (exp (- (exp x) 1.0))) x)
6.0ms	(log (exp (- (exp x) 1.0)))
5.0ms	(- (exp x) 1.0)

series74.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (log (exp (- (exp x) 1.0))) x)
14.0ms	(log (exp (- (exp x) 1.0)))
15.0ms	(- (exp x) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	356	867
1	1076	659
2	5002	584

prune154.0ms

Filtered

122 candidates to 77 candidates (63.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	3	125

Merged error: 0.0b

Counts

125 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (cbrt (pow (- (exp x) 1.0) 3)) x)
0.0b	(pow (- (exp x) 1.0) 3)
0.0b	(cbrt (pow (- (exp x) 1.0) 3))
3.9b	(- (exp x) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

80×	`cbrt-prod`
79×	`add-sqr-sqrt` `*-un-lft-identity`
57×	`times-frac`
53×	`add-cube-cbrt`
30×	`unpow-prod-down` `cube-prod`
19×	`associate-/l*`
13×	`distribute-lft-out--` `difference-of-squares`
9×	`prod-diff`
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-neg` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `div-exp` `pow-exp` `clear-num` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 183

Calls

4 calls:

9.0ms	(/ (cbrt (pow (- (exp x) 1.0) 3)) x)
5.0ms	(pow (- (exp x) 1.0) 3)
5.0ms	(cbrt (pow (- (exp x) 1.0) 3))
5.0ms	(- (exp x) 1.0)

series112.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (cbrt (pow (- (exp x) 1.0) 3)) x)
38.0ms	(pow (- (exp x) 1.0) 3)
14.0ms	(cbrt (pow (- (exp x) 1.0) 3))
15.0ms	(- (exp x) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	450	1387
1	1791	1221
2	5001	1188

prune224.0ms

Filtered

195 candidates to 100 candidates (51.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	194	4	198

Merged error: 0.0b

Counts

198 → 4

regimes24.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.2b

bsearch26.0ms

Steps

Iters	Range		Point
9	-3.7752751361666412	-2.6386627092684764e-08	-0.00018411700096191634

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample870.0ms

Algorithm

intervals

Results

377.0ms	2220×	body	1280	valid
173.0ms	1659×	body	640	valid
104.0ms	5379×	body	80	valid
62.0ms	878×	body	320	valid
19.0ms	420×	body	160	valid