Details

sample300.0ms

Algorithm

intervals

Results

14.0ms	362×	body	80	nan
12.0ms	235×	body	80	valid
8.0ms	216×	body	80	overflowed
2.0ms	23×	body	160	valid

simplify76.0ms

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: 4.0b

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))
4.6b	(- (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:

22.0ms	(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)

series204.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
63.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
27.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (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

prune341.0ms

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

4.0ms	(+ (exp x) 1.0)
13.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
1.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
5.0ms	(- (exp (* 2.0 x)) 1.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+ (exp x) 1.0)
159.0ms	(sqrt (* (/ (- (exp (* 2.0 x)) 1.0) (fma (- 1.0) 1.0 (exp (+ x x)))) (+ (exp x) 1.0)))
42.0ms	(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	5001	559

prune239.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0b

Counts

88 → 3

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)))
4.6b	(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	(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)

series248.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(log1p (+ (exp x) 1.0))
110.0ms	(expm1 (log1p (+ (exp x) 1.0)))
45.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (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

prune219.0ms

Filtered

72 candidates to 52 candidates (72.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0b

Counts

75 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.3b	(/ (pow x 2) (sqrt 2.0))
0.4b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.4b	(/ x (sqrt 2.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

177×	`times-frac`
176×	`add-sqr-sqrt`
151×	`*-un-lft-identity`
149×	`add-cube-cbrt`
78×	`prod-diff`
67×	`sqrt-prod`
52×	`associate-l`
41×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
21×	`add-exp-log`
15×	`unpow2` `sqr-pow`
13×	`add-cbrt-cube`
12×	`associate-/r*`
11×	`associate-/l*`
9×	`div-inv` `add-log-exp` `unswap-sqr`
7×	`div-exp`
6×	`pow1` `associate-r`
4×	`expm1-log1p-u` `associate-*r/` `prod-exp` `log1p-expm1-u`
3×	`cbrt-undiv` `sum-log`
2×	`frac-times` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `frac-add` `pow-exp` `clear-num` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`
1×	`+-commutative` `associate-+r+` `fma-def` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out--`

Counts

4 → 308

Calls

4 calls:

9.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
6.0ms	(/ (pow x 2) (sqrt 2.0))
24.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
7.0ms	(/ x (sqrt 2.0))

series290.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
64.0ms	(/ (pow x 2) (sqrt 2.0))
72.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
58.0ms	(/ x (sqrt 2.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1334	4318
1	5001	3448

prune516.0ms

Filtered

320 candidates to 163 candidates (50.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	320	3	323

Merged error: 0b

Counts

323 → 3

regimes23.0ms

Accuracy

75.8% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.0b

bsearch27.0ms

Steps

Iters	Range		Point
4	-9.044545662313305e-16	-5.385337346103337e-16	-7.286058249866369e-16

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	39	24

end0.0ms

sample1.5s

Algorithm

intervals

Results

496.0ms	12370×	body	80	nan
316.0ms	7368×	body	80	valid
247.0ms	6473×	body	80	overflowed
77.0ms	762×	body	160	valid