Details

sample102.0ms

Algorithm

intervals

Results

38.0ms	80×	body	1280	valid
21.0ms	80×	body	640	valid
14.0ms	241×	body	80	valid
8.0ms	46×	body	320	valid
2.0ms	19×	body	160	valid

simplify365.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	9
1	41	9
2	83	9
3	173	9
4	271	9
5	533	9
6	1023	9
7	1395	9
8	4369	9
9	5002	9

prune3.0ms

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: 20.7b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.0b	(- (exp l) (exp (- l)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
8×	`associate-r`
6×	`add-cube-cbrt`
5×	`add-log-exp`
4×	`associate-r/` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `flip3--` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

3 → 60

Calls

3 calls:

7.0ms	(* J (- (exp l) (exp (- l))))
9.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
5.0ms	(- (exp l) (exp (- l)))

series180.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* J (- (exp l) (exp (- l))))
89.0ms	(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
39.0ms	(- (exp l) (exp (- l)))

simplify37.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	264	566
1	1116	481
2	5002	475

prune179.0ms

Filtered

69 candidates to 47 candidates (68.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	2	70

Merged error: 0.0b

Counts

70 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
0.1b	(* 1/60 (pow l 5))
0.1b	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
10×	`associate-l` `prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `associate-r/` `pow-prod-down` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*l/` `pow-exp` `flip-+`
1×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3`

Counts

4 → 98

Calls

4 calls:

9.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
5.0ms	(* 1/60 (pow l 5))
14.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series375.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))))
51.0ms	(* 1/60 (pow l 5))
161.0ms	(* (* J (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l)))) (cos (/ K 2.0)))
35.0ms	(* 1/3 (pow l 3))

simplify73.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	464	817
1	2375	697
2	5001	697

prune302.0ms

Filtered

110 candidates to 70 candidates (63.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	108	4	112

Merged error: 0.0b

Counts

112 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/60 (pow l 5))
0.1b	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
0.1b	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
0.1b	(* 1/3 (pow l 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`associate-r`
21×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-l`
11×	`pow1`
10×	`prod-exp`
8×	`unpow-prod-down` `unswap-sqr`
6×	`cbrt-unprod`
4×	`cube-prod` `pow-prod-down` `associate-l/` `-commutative` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+`
1×	`cube-mult` `unpow3`

Counts

4 → 96

Calls

4 calls:

5.0ms	(* 1/60 (pow l 5))
14.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
10.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
6.0ms	(* 1/3 (pow l 3))

series332.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* 1/60 (pow l 5))
159.0ms	(* J (* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0))))
87.0ms	(* (+ (* 1/3 (pow l 3)) (+ (* 1/60 (pow l 5)) (* 2 l))) (cos (/ K 2.0)))
35.0ms	(* 1/3 (pow l 3))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	444	856
1	2079	731
2	5001	731

prune426.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	108	4	112

Merged error: 0.0b

Counts

112 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp l) 3) (pow (exp (- l)) 3)) (+ (+ 1 (exp (+ l l))) (pow (exp l) -2)))
0.1b	(pow (exp l) 3)
0.1b	(pow (exp (- l)) 3)
5.7b	(- (pow (exp l) 3) (pow (exp (- l)) 3))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

246×	`*-un-lft-identity`
214×	`add-sqr-sqrt`
125×	`times-frac`
112×	`difference-of-squares`
90×	`unpow-prod-down` `cube-prod`
78×	`distribute-lft-out`
58×	`sqr-pow`
46×	`add-cube-cbrt`
35×	`distribute-lft-out--`
25×	`associate-/l*`
15×	`pow-pow`
13×	`exp-prod`
8×	`add-cbrt-cube`
7×	`difference-cubes`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`associate-/r*`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`cube-div` `cube-mult` `pow-to-exp` `flip3--` `unpow3` `pow-exp` `associate-/r/` `flip--` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-undiv` `neg-sub0` `exp-neg` `neg-mul-1` `sub-neg` `frac-2neg` `flip3-+` `exp-diff` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 267

Calls

4 calls:

26.0ms	(/ (- (pow (exp l) 3) (pow (exp (- l)) 3)) (+ (+ 1 (exp (+ l l))) (pow (exp l) -2)))
3.0ms	(pow (exp l) 3)
5.0ms	(pow (exp (- l)) 3)
14.0ms	(- (pow (exp l) 3) (pow (exp (- l)) 3))

series305.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(/ (- (pow (exp l) 3) (pow (exp (- l)) 3)) (+ (+ 1 (exp (+ l l))) (pow (exp l) -2)))
22.0ms	(pow (exp l) 3)
28.0ms	(pow (exp (- l)) 3)
91.0ms	(- (pow (exp l) 3) (pow (exp (- l)) 3))

simplify141.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	656	4532
1	2826	4419
2	5003	4203

prune600.0ms

Filtered

279 candidates to 111 candidates (39.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	278	5	283

Merged error: 0b

Counts

283 → 5

regimes203.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	12
1	30	12

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.1s	2691×	body	1280	valid
677.0ms	2612×	body	640	valid
462.0ms	8268×	body	80	valid
246.0ms	1397×	body	320	valid
87.0ms	770×	body	160	valid

Details

sample102.0ms

simplify365.0ms

prune3.0ms

localize13.0ms

rewrite22.0ms

series180.0ms

simplify37.0ms

prune179.0ms

localize17.0ms

rewrite37.0ms

series375.0ms

simplify73.0ms

prune302.0ms

localize17.0ms

rewrite37.0ms

series332.0ms

simplify66.0ms

prune426.0ms

localize23.0ms

rewrite63.0ms

series305.0ms

simplify141.0ms

prune600.0ms

regimes203.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling