Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	80×	body	1280	valid
3.0ms	36×	body	640	valid
3.0ms	158×	body	80	valid
2.0ms	31×	body	320	valid
1.0ms	12×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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
done	5001	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.7b	(- (exp (* a x)) 1.0)

rewrite19.0ms

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:

4.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series53.0ms

Counts

2 → 6

Calls

2 calls:

14.0ms	(exp (* a x))
40.0ms	(- (exp (* a x)) 1.0)

simplify84.0ms

Counts

46 → 46

Iterations

Useful iterations: 3 (81.0ms)

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

prune98.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.1b	(pow (- (exp (* a x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
4.7b	(- (exp (* a x)) 1.0)

rewrite53.0ms

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:

4.0ms	(exp (* a x))
19.0ms	(pow (- (exp (* a x)) 1.0) 3)
14.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
14.0ms	(- (exp (* a x)) 1.0)

series139.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(exp (* a x))
55.0ms	(pow (- (exp (* a x)) 1.0) 3)
35.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
35.0ms	(- (exp (* a x)) 1.0)

simplify45.0ms

Counts

112 → 112

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	333	725
1	1336	625
2	5002	613
done	5002	613

prune218.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)
0.0b	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
0.1b	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))
4.7b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite272.0ms

Algorithm

rewrite-expression-head

Rules

938×	`add-sqr-sqrt`
895×	`unpow-prod-down` `cube-prod`
676×	`cbrt-prod`
672×	`times-frac`
560×	`*-un-lft-identity`
432×	`difference-of-squares`
311×	`sqr-pow`
290×	`add-cube-cbrt`
144×	`prod-diff`
135×	`distribute-lft-out--`
95×	`cube-mult` `unpow3`
27×	`difference-cubes`
12×	`fma-neg`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `pow1/3` `diff-log` `div-inv`

Counts

4 → 975

Calls

4 calls:

3.0ms	(pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)
51.0ms	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
82.0ms	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))
46.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series326.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)
74.0ms	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
124.0ms	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))
55.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify256.0ms

Counts

987 → 987

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1619	28177
1	5002	26928
done	5002	26928

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)
0.0b	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
0.1b	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (* (sqrt (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)) (sqrt (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))))
4.7b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

209×	`add-sqr-sqrt`
188×	`unpow-prod-down` `cube-prod`
144×	`prod-diff`
139×	`*-un-lft-identity`
89×	`add-cube-cbrt`
80×	`difference-of-squares`
68×	`sqr-pow`
60×	`cbrt-prod`
56×	`times-frac`
28×	`cube-mult` `unpow3`
25×	`distribute-lft-out--`
12×	`fma-neg`
6×	`pow1` `add-exp-log` `pow-unpow` `add-cbrt-cube` `add-log-exp`
5×	`difference-cubes`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cube-div` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `pow1/3` `diff-log` `div-inv`

Counts

4 → 359

Calls

4 calls:

2.0ms	(pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)
47.0ms	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
57.0ms	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (* (sqrt (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)) (sqrt (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))))
46.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series314.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)
72.0ms	(pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3)
119.0ms	(cbrt (/ (pow (- (pow (exp (* a x)) 3) (pow 1.0 3)) 3) (* (sqrt (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)) (sqrt (pow (fma 1.0 (+ (exp (* a x)) 1.0) (exp (+ (* a x) (* a x)))) 3)))))
53.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify156.0ms

Counts

371 → 371

Iterations

Useful iterations: 2 (101.0ms)

Iter	Nodes	Cost
0	949	6393
1	3548	5455
2	5001	5434
done	5001	5434

prune632.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.1b

regimes222.0ms

Accuracy

93.4% (1.4b remaining)

Error of 9.7b against oracle of 8.4b and baseline of 28.8b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	46
1	43	46
done	43	46

end0.0ms

sample943.0ms

Algorithm

intervals

Results

393.0ms	2631×	body	1280	valid
121.0ms	1269×	body	640	valid
107.0ms	5623×	body	80	valid
52.0ms	771×	body	320	valid
17.0ms	390×	body	160	valid