Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	82×	body	1280	valid
4.0ms	37×	body	640	valid
3.0ms	184×	body	80	valid
2.0ms	26×	body	320	valid
1.0ms	15×	body	160	valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	3
7	5001	3

prune2.0ms

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: 27.8b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.6b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

2.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series49.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(exp (* a x))
32.0ms	(- (exp (* a x)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune67.0ms

Filtered

30 candidates to 20 candidates (66.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	24	6	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	6	31

Merged error: 8.3b

Counts

31 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* a x)) 1.0)
0.0b	(pow (exp (* a x)) 3)
0.0b	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
4.6b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-sqr-sqrt`
89×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
63×	`unpow-prod-down` `cube-prod`
41×	`sqr-pow`
37×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
9×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`add-exp-log`
5×	`pow1` `difference-cubes`
3×	`pow-unpow` `pow-pow` `associate-/r*`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `unpow3` `div-sub` `div-exp` `pow-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 191

Calls

4 calls:

4.0ms	(+ (exp (* a x)) 1.0)
3.0ms	(pow (exp (* a x)) 3)
25.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
11.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series204.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (exp (* a x)) 1.0)
23.0ms	(pow (exp (* a x)) 3)
114.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
51.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify104.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	629	3736
1	2568	3651
2	5002	3644

prune581.0ms

Filtered

203 candidates to 106 candidates (52.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	198	5	203
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	202	7	209

Merged error: 8.3b

Counts

209 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (* a x) 3))
0.0b	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
0.2b	(* (* a x) 3)
4.6b	(- (exp (* (* a x) 3)) (pow 1.0 3))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
33×	`times-frac`
31×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`difference-of-squares`
15×	`difference-cubes`
13×	`add-log-exp`
11×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`pow1`
6×	`exp-lft-cube` `exp-prod` `exp-to-pow`
5×	`unpow-prod-down` `cube-prod` `distribute-lft-out--` `sqr-pow`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 113

Calls

4 calls:

2.0ms	(exp (* (* a x) 3))
15.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
5.0ms	(* (* a x) 3)
6.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

series177.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(exp (* (* a x) 3))
97.0ms	(/ (- (exp (* (* a x) 3)) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
21.0ms	(* (* a x) 3)
42.0ms	(- (exp (* (* a x) 3)) (pow 1.0 3))

simplify69.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	507	1961
1	2098	1858
2	5002	1853

prune314.0ms

Filtered

125 candidates to 79 candidates (63.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Merged error: 8.3b

Counts

132 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp (* a x)) 6)
0.2b	(* (* a x) 3)
0.2b	(* (* a x) 3)
4.5b	(- (pow (exp (* (* a x) 3)) 3) (pow (pow 1.0 3) 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
41×	`unpow-prod-down`
40×	`difference-of-squares`
38×	`cube-prod`
23×	`sqr-pow`
18×	`*-un-lft-identity`
15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
7×	`add-log-exp`
6×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`distribute-lft-out--`
3×	`pow-unpow` `pow-pow`
2×	`associate-l` `*-commutative`
1×	`difference-cubes` `pow-to-exp` `sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `pow-exp` `flip--`

Counts

4 → 113

Calls

4 calls:

3.0ms	(pow (exp (* a x)) 6)
5.0ms	(* (* a x) 3)
5.0ms	(* (* a x) 3)
23.0ms	(- (pow (exp (* (* a x) 3)) 3) (pow (pow 1.0 3) 3))

series132.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (exp (* a x)) 6)
18.0ms	(* (* a x) 3)
18.0ms	(* (* a x) 3)
62.0ms	(- (pow (exp (* (* a x) 3)) 3) (pow (pow 1.0 3) 3))

simplify68.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	417	1110
1	1812	1069
2	5001	1063

prune363.0ms

Filtered

125 candidates to 63 candidates (50.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	125	8	133

Merged error: 8.3b

Counts

133 → 8

regimes314.0ms

Accuracy

94.1% (1.2b remaining)

Error of 9.3b against oracle of 8.1b and baseline of 28.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	36
1	45	36

end0.0ms

sample907.0ms

Algorithm

intervals

Results

413.0ms	2664×	body	1280	valid
128.0ms	1278×	body	640	valid
103.0ms	5498×	body	80	valid
51.0ms	791×	body	320	valid
22.0ms	394×	body	160	valid