Details

sample320.0ms

Algorithm

intervals

Results

37.0ms	183×	body	10240	exit
10.0ms	323×	body	80	nan
8.0ms	238×	body	80	valid
2.0ms	19×	body	160	valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	41	7
3	75	7
4	182	7
5	576	7
6	2666	7
7	5001	7

prune4.0ms

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: 4.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.6b	(- (exp (* 2.0 x)) 1.0)
4.8b	(- (exp x) 1.0)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

92×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
51×	`times-frac`
41×	`add-cube-cbrt`
31×	`sqrt-prod`
24×	`distribute-lft-out--` `difference-of-squares`
18×	`prod-diff`
8×	`add-log-exp`
6×	`add-exp-log` `fma-neg` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 155

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
10.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series202.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify59.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	480	1694
1	1523	1484
2	5001	1470

prune333.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	164	3	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	165	3	168

Merged error: 0.0b

Counts

168 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
0.0b	(+ (exp x) 1.0)
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(- (exp (* 2.0 x)) 1.0)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`prod-diff`
8×	`add-log-exp`
7×	`pow1`
5×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-def` `flip3-+` `fma-neg` `flip-+`
2×	`frac-times` `sqrt-pow1` `associate-*r/`
1×	`+-commutative` `sub-neg` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-*l/` `sum-log` `sqrt-prod` `flip--` `fma-udef` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 73

Calls

4 calls:

9.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
4.0ms	(+ (exp x) 1.0)
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series232.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
8.0ms	(+ (exp x) 1.0)
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	361	673
1	1258	564
2	5002	559

prune237.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	84	4	88

Merged error: 0b

Counts

88 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (+ (exp x) 1.0)))
0.1b	(log1p (+ (exp x) 1.0))
4.6b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.6b	(- (exp (* 2.0 x)) 1.0)

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`add-log-exp`
5×	`expm1-log1p-u`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
1×	`sub-neg` `log1p-udef` `expm1-log1p` `flip3--` `diff-log` `log1p-expm1` `flip--` `fma-udef` `distribute-lft-out--` `expm1-udef` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

1.0ms	(expm1 (log1p (+ (exp x) 1.0)))
1.0ms	(log1p (+ (exp x) 1.0))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series247.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(expm1 (log1p (+ (exp x) 1.0)))
70.0ms	(log1p (+ (exp x) 1.0))
39.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify107.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	266	460
1	819	351
2	3757	340
3	5001	325

prune218.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	72	4	76

Merged error: 0b

Counts

76 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* 2.0 x)))
0.0b	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
4.8b	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
4.8b	(- (exp x) 1.0)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

2.0ms	(sqrt (exp (* 2.0 x)))
6.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
1.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
5.0ms	(- (exp x) 1.0)

series245.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (exp (* 2.0 x)))
120.0ms	(/ (fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0)) (- (exp x) 1.0))
87.0ms	(fma (sqrt (exp (* 2.0 x))) (sqrt (exp (* 2.0 x))) (- 1.0))
15.0ms	(- (exp x) 1.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	305	1109
1	943	913
2	5001	891

prune241.0ms

Filtered

106 candidates to 77 candidates (72.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	106	4	110

Merged error: 0b

Counts

110 → 4

regimes26.0ms

Accuracy

70.5% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.6b

bsearch45.0ms

Steps

Iters	Range		Point
7	-1.3081950593114417e-10	-7.983923007473122e-12	-4.651059556366224e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	16
1	27	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6682×	body	10240	exit
379.0ms	12570×	body	80	nan
243.0ms	7391×	body	80	valid
63.0ms	728×	body	160	valid