Details

sample298.0ms

Algorithm

intervals

Results

15.0ms	367×	body	80	nan
10.0ms	237×	body	80	valid
7.0ms	186×	body	80	overflowed
2.0ms	22×	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: 3.9b

Counts

2 → 1

localize11.0ms

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))
4.5b	(- (exp (* 2.0 x)) 1.0)
4.7b	(- (exp x) 1.0)

rewrite51.0ms

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:

23.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
9.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series196.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp x) 1.0)

simplify58.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (41.0ms)

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

prune339.0ms

Filtered

167 candidates to 110 candidates (65.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	163	4	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	164	4	168

Merged error: 0.0b

Counts

168 → 4

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)
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (exp (* 2.0 x)) 1.0)

rewrite24.0ms

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)))
8.0ms	(- (exp (* 2.0 x)) 1.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
11.0ms	(+ (exp x) 1.0)
41.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify48.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

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

prune238.0ms

Filtered

85 candidates to 65 candidates (76.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 0b

Counts

89 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (+ (exp x) 1.0))
0.1b	(expm1 (log1p (+ (exp x) 1.0)))
4.5b	(fma (- 1.0) 1.0 (exp (+ x x)))
4.5b	(- (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	(log1p (+ (exp x) 1.0))
1.0ms	(expm1 (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:

64.0ms	(log1p (+ (exp x) 1.0))
115.0ms	(expm1 (log1p (+ (exp x) 1.0)))
40.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
28.0ms	(- (exp (* 2.0 x)) 1.0)

simplify106.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (99.0ms)

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

prune223.0ms

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

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
24.6b	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

2 → 25

Calls

2 calls:

1.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
2.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

series100.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(fma 0.5 (pow x 2) (fma 1.0 x 2.0))
79.0ms	(sqrt (fma 0.5 (pow x 2) (fma 1.0 x 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (63.0ms)

Iter	Nodes	Cost
0	139	185
1	458	173
2	2447	165
3	5001	162

prune70.0ms

Filtered

31 candidates to 25 candidates (80.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	31	0	31
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	31	4	35

Merged error: 0b

Counts

35 → 4

regimes31.0ms

Accuracy

69.2% (0.8b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 2.8b

bsearch44.0ms

Steps

Iters	Range		Point
8	-4.426567571666705e-08	-1.1436914135067998e-11	-3.2476974448659e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	16
1	27	16

end0.0ms

sample1.4s

Algorithm

intervals

Results

475.0ms	12468×	body	80	nan
303.0ms	7372×	body	80	valid
255.0ms	6686×	body	80	overflowed
73.0ms	747×	body	160	valid