Details

sample314.0ms

Algorithm

intervals

Results

36.0ms	187×	body	10240	exit
10.0ms	358×	body	80	nan
9.0ms	243×	body	80	valid
1.0ms	17×	body	160	valid

simplify73.0ms

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

prune17.0ms

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)))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.7b	(- (exp (* 2.0 x)) 1.0)
3.8b	(- (exp x) 1.0)

rewrite39.0ms

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)
7.0ms	(- (exp x) 1.0)

series208.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
58.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
33.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (43.0ms)

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

prune342.0ms

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: 0.2b

Counts

168 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.3b	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
3.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.7b	(- (exp (* 2.0 x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

174×	`times-frac`
171×	`*-un-lft-identity`
127×	`add-sqr-sqrt`
87×	`add-cube-cbrt`
22×	`associate-/r*` `distribute-lft-out`
20×	`distribute-lft-out--` `difference-of-squares`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
9×	`prod-diff`
8×	`div-inv` `associate-/l*`
7×	`flip3-+` `flip-+`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 206

Calls

4 calls:

6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
14.0ms	(/ (- (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)

series258.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
116.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
48.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify116.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	805	3596
1	3551	3384
2	5003	3382

prune561.0ms

Filtered

218 candidates to 147 candidates (67.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	219	3	222

Merged error: 0.2b

Counts

222 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
0.3b	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
3.7b	(fma (- 1.0) 1.0 (exp (+ x x)))
3.7b	(- (exp (* 2.0 x)) 1.0)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

594×	`times-frac`
462×	`*-un-lft-identity`
334×	`add-sqr-sqrt`
304×	`cbrt-prod`
256×	`add-cube-cbrt`
95×	`unpow-prod-down` `cube-prod`
64×	`distribute-lft-out`
43×	`associate-/r/`
39×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r` `div-inv` `associate-/l`
21×	`flip3-+` `flip-+`
19×	`cube-mult` `unpow3` `sqr-pow`
11×	`add-exp-log`
9×	`prod-diff` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-neg`
2×	`cube-div` `cbrt-div` `flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `fma-udef`

Counts

4 → 471

Calls

4 calls:

6.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
22.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (/ (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)

series251.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0))
114.0ms	(/ (cbrt (pow (- (exp (* 2.0 x)) 1.0) 3)) (/ (fma (- 1.0) 1.0 (exp (+ x x))) (+ (exp x) 1.0)))
46.0ms	(fma (- 1.0) 1.0 (exp (+ x x)))
25.0ms	(- (exp (* 2.0 x)) 1.0)

simplify117.0ms

Algorithm

egg-herbie

Counts

483 → 483

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1153	10492
1	5001	10070

prune841.0ms

Filtered

483 candidates to 198 candidates (41.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	483	0	483
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	483	3	486

Merged error: 0.2b

Counts

486 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* 0.5 (/ x (sqrt 2.0))) (+ (sqrt 2.0) (* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))))
0.2b	(/ (pow x 2) (sqrt 2.0))
0.4b	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
0.5b	(/ x (sqrt 2.0))

rewrite64.0ms

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:

10.0ms	(+ (* 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))
27.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
4.0ms	(/ x (sqrt 2.0))

series293.0ms

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)))))
63.0ms	(/ (pow x 2) (sqrt 2.0))
73.0ms	(* (/ (pow x 2) (sqrt 2.0)) (- 0.25 (/ 0.125 2.0)))
62.0ms	(/ x (sqrt 2.0))

simplify74.0ms

Algorithm

egg-herbie

Counts

320 → 320

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1334	4318
1	5001	3448

prune516.0ms

Filtered

320 candidates to 163 candidates (50.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	319	1	320
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	320	3	323

Merged error: 0.2b

Counts

323 → 3

regimes25.0ms

Accuracy

73.1% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.1b

bsearch49.0ms

Steps

Iters	Range		Point
6	-4.345123270967491e-17	-6.5315291284408596e-18	-4.0542415267134493e-17

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	36
1	48	36

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	6438×	body	10240	exit
352.0ms	12360×	body	80	nan
226.0ms	7366×	body	80	valid
56.0ms	752×	body	160	valid