Details

sample31.0ms

Algorithm

intervals

Results

14.0ms	88×	body	1280	valid
4.0ms	39×	body	640	valid
3.0ms	175×	body	80	valid
1.0ms	20×	body	320	valid
1.0ms	13×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	27	3
3	50	3
4	115	3
5	329	3
6	1642	3
7	5001	3

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.4b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series51.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify81.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	173	292
1	562	211
2	2710	200
3	5002	164

prune93.0ms

Filtered

46 candidates to 28 candidates (60.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
0.1b	(pow (- (exp (* a x)) 1.0) 3)
3.4b	(- (exp (* a x)) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`cbrt-prod`
10×	`unpow-prod-down` `cube-prod`
9×	`prod-diff`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `flip3--` `fma-neg` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

1.0ms	(exp (* a x))
6.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
6.0ms	(pow (- (exp (* a x)) 1.0) 3)
5.0ms	(- (exp (* a x)) 1.0)

series134.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (* a x))
33.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
49.0ms	(pow (- (exp (* a x)) 1.0) 3)
37.0ms	(- (exp (* a x)) 1.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	333	721
1	1342	623
2	5001	613

prune202.0ms

Filtered

112 candidates to 61 candidates (54.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3)
0.0b	(pow (+ (exp (* a x)) 1.0) 3)
0.0b	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
3.3b	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

202×	`cbrt-prod`
196×	`times-frac`
155×	`*-un-lft-identity`
120×	`unpow-prod-down` `cube-prod`
95×	`add-sqr-sqrt` `add-cube-cbrt`
31×	`difference-of-squares`
30×	`cube-mult` `unpow3` `distribute-lft-out` `sqr-pow`
6×	`pow1` `add-exp-log` `cube-div` `pow-unpow` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`pow-to-exp` `flip3--` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip--` `flip-+` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `fma-neg` `pow1/3` `diff-log` `prod-diff` `div-inv`

Counts

4 → 288

Calls

4 calls:

9.0ms	(pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3)
6.0ms	(pow (+ (exp (* a x)) 1.0) 3)
24.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
6.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

series208.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3)
31.0ms	(pow (+ (exp (* a x)) 1.0) 3)
68.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
45.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

simplify169.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	832	6475
1	4324	6256
2	5001	6253

prune468.0ms

Filtered

300 candidates to 116 candidates (38.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp (* a x)) 3)
0.0b	(/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (fma (pow (exp (* a x)) 3) (exp (* a x)) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2)))) 3))
0.0b	(cbrt (/ (/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (fma (pow (exp (* a x)) 3) (exp (* a x)) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2)))) 3)) (pow (+ (exp (* a x)) 1.0) 3)))
3.3b	(- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

16760×	`times-frac`
11208×	`unpow-prod-down` `cube-prod`
8126×	`cbrt-prod`
7531×	`*-un-lft-identity`
7389×	`add-sqr-sqrt`
5808×	`difference-of-squares`
4485×	`add-cube-cbrt`
4404×	`sqr-pow`
1500×	`cube-mult` `unpow3`
1160×	`distribute-lft-out`
363×	`difference-cubes` `distribute-lft-out--`
64×	`prod-diff`
48×	`associate-/l*`
16×	`add-exp-log` `div-inv`
12×	`associate-/r*`
9×	`div-exp`
8×	`fma-neg`
7×	`pow-to-exp` `pow-exp` `add-cbrt-cube` `add-log-exp`
5×	`pow1`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `pow-pow`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `cbrt-div` `exp-prod` `exp-to-pow` `frac-2neg` `flip3-+` `pow1/3` `diff-log` `clear-num` `flip-+` `rem-cube-cbrt`

Counts

4 → 8928

Calls

4 calls:

2.0ms	(pow (exp (* a x)) 3)
72.0ms	(/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (fma (pow (exp (* a x)) 3) (exp (* a x)) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2)))) 3))
517.0ms	(cbrt (/ (/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (fma (pow (exp (* a x)) 3) (exp (* a x)) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2)))) 3)) (pow (+ (exp (* a x)) 1.0) 3)))
15.0ms	(- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3))

series500.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (exp (* a x)) 3)
212.0ms	(/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (fma (pow (exp (* a x)) 3) (exp (* a x)) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2)))) 3))
189.0ms	(cbrt (/ (/ (pow (- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3)) 3) (pow (fma (pow (exp (* a x)) 3) (exp (* a x)) (* (* 1.0 1.0) (+ (* 1.0 1.0) (pow (exp (* a x)) 2)))) 3)) (pow (+ (exp (* a x)) 1.0) 3)))
71.0ms	(- (pow (* (exp (* a x)) (exp (* a x))) 3) (pow (* 1.0 1.0) 3))

simplify4.8s

Algorithm

egg-herbie

Counts

8940 → 8940

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5892	562357

prune11.0s

Filtered

8940 candidates to 1486 candidates (16.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

regimes334.0ms

Accuracy

92.7% (1.6b remaining)

Error of 10.2b against oracle of 8.6b and baseline of 30.3b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	35
1	44	35

end0.0ms

sample893.0ms

Algorithm

intervals

Results

413.0ms	2708×	body	1280	valid
133.0ms	1360×	body	640	valid
104.0ms	5445×	body	80	valid
48.0ms	788×	body	320	valid
17.0ms	394×	body	160	valid