Details

sample36.0ms

Algorithm

intervals

Results

12.0ms	67×	body	1280	valid
7.0ms	56×	body	640	valid
6.0ms	174×	body	80	valid
2.0ms	28×	body	320	valid
1.0ms	21×	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: 41.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- (exp x) 1.0) x)
6.2b	(- (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-/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)

series54.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ (- (exp x) 1.0) x)
14.0ms	(- (exp x) 1.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 2 (28.0ms)

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

prune112.0ms

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

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(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))

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

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

simplify25.0ms

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

prune27.0ms

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 4 expressions with local error:

0.0b	(+ (exp x) 1.0)
0.0b	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
0.0b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
6.1b	(fma (- 1.0) 1.0 (exp (+ x x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
65×	`add-sqr-sqrt` `add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log` `fma-udef` `associate-/l/`

Counts

4 → 154

Calls

4 calls:

4.0ms	(+ (exp x) 1.0)
9.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
102.0ms	(/ (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)) x)
68.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	531	2009
1	1917	1909
2	5001	1904

prune349.0ms

Filtered

166 candidates to 127 candidates (76.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	166	3	169

Merged error: 0.0b

Counts

169 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (exp x) 1.0) (/ 1 x))
6.2b	(- (exp x) 1.0)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
17×	`add-cube-cbrt`
13×	`associate-r`
11×	`add-exp-log` `times-frac`
9×	`prod-diff`
7×	`add-cbrt-cube`
5×	`associate-l`
4×	`pow1` `prod-exp` `add-log-exp`
3×	`flip3--` `fma-neg` `flip--` `unswap-sqr`
2×	`expm1-log1p-u` `frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `sub-neg` `rec-exp` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

2 → 72

Calls

2 calls:

10.0ms	(* (- (exp x) 1.0) (/ 1 x))
4.0ms	(- (exp x) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* (- (exp x) 1.0) (/ 1 x))
14.0ms	(- (exp x) 1.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	347	486
1	1452	375
2	5001	356

prune96.0ms

Filtered

78 candidates to 52 candidates (66.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	78	3	81

Merged error: 0.0b

Counts

81 → 3

regimes20.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 22.2b

bsearch36.0ms

Steps

Iters	Range		Point
10	-55383.34621353126	-7.537518413748392e-06	-0.00013197879371292656

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	17
1	26	17

end0.0ms

sample1.0s

Algorithm

intervals

Results

430.0ms	2210×	body	1280	valid
200.0ms	1602×	body	640	valid
134.0ms	5614×	body	80	valid
65.0ms	798×	body	320	valid
23.0ms	436×	body	160	valid