Details

sample45.0ms

Algorithm

intervals

Results

19.0ms	72×	body	1280	valid
7.0ms	190×	body	80	valid
6.0ms	38×	body	640	valid
3.0ms	30×	body	320	valid
1.0ms	12×	body	160	valid

simplify62.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.7b

localize5.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
4.4b	(- (exp (* a x)) 1.0)

rewrite5.0ms

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:

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

series46.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
34.0ms	(- (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

prune73.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (exp (* a x)) 1.0))
4.4b	(- (exp (* a x)) 1.0)
4.4b	(- (exp (* a x)) 1.0)
4.4b	(- (exp (* a x)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (- (exp (* a x)) 1.0))
4.0ms	(- (exp (* a x)) 1.0)
4.0ms	(- (exp (* a x)) 1.0)
4.0ms	(- (exp (* a x)) 1.0)

series197.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (- (exp (* a x)) 1.0))
32.0ms	(- (exp (* a x)) 1.0)
37.0ms	(- (exp (* a x)) 1.0)
33.0ms	(- (exp (* a x)) 1.0)

simplify63.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 3 (57.0ms)

Iter	Nodes	Cost
0	167	460
1	491	412
2	1911	395
3	5001	391

prune192.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* a x))
0.1b	(exp (* a x))
0.3b	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
4.4b	(- (pow (exp (* a x)) 3) (pow 1.0 3))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-sqr-sqrt`
84×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
60×	`unpow-prod-down` `cube-prod`
40×	`sqr-pow`
34×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`difference-cubes`
4×	`pow1`
3×	`associate-/r*`
2×	`exp-prod` `flip3--` `exp-to-pow` `associate-/r/` `flip--` `rem-exp-log` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 174

Calls

4 calls:

1.0ms	(exp (* a x))
1.0ms	(exp (* a x))
58.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
18.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

series194.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
12.0ms	(exp (* a x))
114.0ms	(/ (- (pow (exp (* a x)) 3) (pow 1.0 3)) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0)))
57.0ms	(- (pow (exp (* a x)) 3) (pow 1.0 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	556	3551
1	2046	3476
2	5002	3473

prune438.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* a x))
0.1b	(exp (* a x))
0.3b	(/ (- (pow (pow (exp (* a x)) 3) 3) (pow (pow 1.0 3) 3)) (* (+ (+ (pow (exp (* a x)) 6) (pow 1.0 6)) (* (pow (exp (* a x)) 3) (pow 1.0 3))) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))))
4.3b	(- (pow (pow (exp (* a x)) 3) 3) (pow (pow 1.0 3) 3))

rewrite351.0ms

Algorithm

rewrite-expression-head

Rules

468×	`unpow-prod-down` `cube-prod`
426×	`add-sqr-sqrt`
300×	`difference-of-squares`
180×	`sqr-pow`
132×	`*-un-lft-identity`
125×	`times-frac` `associate-/l*`
63×	`distribute-lft-out--`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r/`
6×	`add-cube-cbrt` `flip3-+` `flip-+`
4×	`pow1` `frac-times`
3×	`difference-cubes`
2×	`cbrt-undiv` `exp-prod` `flip3--` `exp-to-pow` `associate-r/` `div-exp` `associate-l/` `flip--` `rem-exp-log` `associate-/l/`
1×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 430

Calls

4 calls:

1.0ms	(exp (* a x))
1.0ms	(exp (* a x))
240.0ms	(/ (- (pow (pow (exp (* a x)) 3) 3) (pow (pow 1.0 3) 3)) (* (+ (+ (pow (exp (* a x)) 6) (pow 1.0 6)) (* (pow (exp (* a x)) 3) (pow 1.0 3))) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))))
74.0ms	(- (pow (pow (exp (* a x)) 3) 3) (pow (pow 1.0 3) 3))

series331.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
12.0ms	(exp (* a x))
240.0ms	(/ (- (pow (pow (exp (* a x)) 3) 3) (pow (pow 1.0 3) 3)) (* (+ (+ (pow (exp (* a x)) 6) (pow 1.0 6)) (* (pow (exp (* a x)) 3) (pow 1.0 3))) (+ (* (exp (* a x)) (+ (exp (* a x)) 1.0)) (* 1.0 1.0))))
68.0ms	(- (pow (pow (exp (* a x)) 3) 3) (pow (pow 1.0 3) 3))

simplify209.0ms

Algorithm

egg-herbie

Counts

442 → 442

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	866	11312
1	3929	11086
2	5001	11086

prune818.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.2b

regimes346.0ms

Accuracy

93.2% (1.4b remaining)

Error of 9.6b against oracle of 8.2b and baseline of 29.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	41
1	56	41

end0.0ms

sample1.3s

Algorithm

intervals

Results

565.0ms	2641×	body	1280	valid
214.0ms	5553×	body	80	valid
195.0ms	1324×	body	640	valid
81.0ms	761×	body	320	valid
32.0ms	410×	body	160	valid