Details

sample343.0ms

Algorithm

intervals

Results

57.0ms	240×	body	10240	exit
14.0ms	421×	body	80	nan
8.0ms	237×	body	80	valid
2.0ms	25×	body	160	valid

simplify74.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 4.9b

Counts

2 → 1

localize12.0ms

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))
5.2b	(- (exp (* 2.0 x)) 1.0)
5.3b	(- (exp x) 1.0)

rewrite40.0ms

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)))
11.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.0ms	(- (exp (* 2.0 x)) 1.0)
8.0ms	(- (exp x) 1.0)

series199.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
56.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
34.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify62.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (41.0ms)

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

prune402.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	162	5	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	163	5	168

Merged error: 0b

Counts

168 → 5

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)
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (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)

series225.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
7.0ms	(+ (exp x) 1.0)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
27.0ms	(- (exp (* 2.0 x)) 1.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (35.0ms)

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

prune281.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	86	4	90

Merged error: 0b

Counts

90 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(sqrt (exp x))
0.4b	(sqrt (exp x))
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
9×	`prod-diff`
8×	`sqrt-pow1`
6×	`pow1` `exp-prod` `sqrt-prod` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`fma-neg`
2×	`rem-sqrt-square` `pow1/2`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 74

Calls

4 calls:

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

series92.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (exp x))
12.0ms	(sqrt (exp x))
44.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
24.0ms	(- (exp (* 2.0 x)) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	219	440
1	605	348
2	2891	335
3	5002	308

prune302.0ms

Filtered

86 candidates to 62 candidates (72.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	86	4	90

Merged error: 0b

Counts

90 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (exp x))
0.5b	(cbrt (exp x))
5.2b	(fma (- 1.0) 1.0 (exp (+ x x)))
5.2b	(- (exp (* 2.0 x)) 1.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

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

series220.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(cbrt (exp x))
76.0ms	(cbrt (exp x))
43.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify92.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	214	444
1	595	344
2	2830	327
3	5001	296

prune271.0ms

Filtered

76 candidates to 56 candidates (73.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	76	4	80

Merged error: 0b

Counts

80 → 4

regimes32.0ms

Accuracy

77.8% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.9b

bsearch42.0ms

Steps

Iters	Range		Point
8	-0.0011167250079306748	-1.485944467815708e-07	-4.034789095259663e-06

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	19
1	27	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	6812×	body	10240	exit
385.0ms	12826×	body	80	nan
247.0ms	7417×	body	80	valid
58.0ms	721×	body	160	valid