Details

sample39.0ms

Algorithm

intervals

Results

20.0ms

776×

body

valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	4
1	41	4
2	102	4
3	224	4
4	401	4
5	758	4
6	2403	4
7	5002	4

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: 7.7b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
7.3b	(/ (* (cosh x) (/ y x)) z)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cosh-def`
8×	`associate-/l/`
7×	`clear-num`
6×	`frac-times` `associate-*r/`
5×	`frac-2neg`
3×	`div-inv` `associate-/l*`
2×	`associate-r` `associate-l/` `un-div-inv` `-commutative`

Counts

3 → 25

Calls

3 calls:

2.0ms	(cosh x)
6.0ms	(* (cosh x) (/ y x))
9.0ms	(/ (* (cosh x) (/ y x)) z)

series243.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(cosh x)
78.0ms	(* (cosh x) (/ y x))
122.0ms	(/ (* (cosh x) (/ y x)) z)

simplify100.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	173	126
1	564	124
2	3452	89
3	5001	89

prune111.0ms

Filtered

34 candidates to 25 candidates (73.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Merged error: 0.0b

Counts

35 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) (- y))
5.8b	(/ (* (+ (exp x) (exp (- x))) (- y)) (* (* -2 x) z))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-commutative`
12×	`times-frac`
8×	`associate-l`
6×	`neg-mul-1` `associate-r`
4×	`associate-l/` `associate-/r`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`distribute-rgt-neg-out` `associate-/l/`
1×	`+-commutative` `frac-2neg` `distribute-frac-neg` `clear-num` `div-inv`

Counts

3 → 33

Calls

3 calls:

3.0ms	(+ (exp x) (exp (- x)))
4.0ms	(* (+ (exp x) (exp (- x))) (- y))
8.0ms	(/ (* (+ (exp x) (exp (- x))) (- y)) (* (* -2 x) z))

series181.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (exp x) (exp (- x)))
62.0ms	(* (+ (exp x) (exp (- x))) (- y))
95.0ms	(/ (* (+ (exp x) (exp (- x))) (- y)) (* (* -2 x) z))

simplify37.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	285	296
1	1004	282
2	5002	274

prune141.0ms

Filtered

42 candidates to 39 candidates (92.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	42	5	47

Merged error: 0.0b

Counts

47 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp x) (exp x))
0.1b	(pow (exp x) 3)
5.8b	(/ (/ (* (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (- y)) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))) (* (* -2 x) z))
8.7b	(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

58×	`exp-neg`
40×	`associate-*r/`
38×	`neg-sub0` `exp-diff`
27×	`frac-sub`
20×	`un-div-inv`
15×	`sub-div`
14×	`associate-l/` `-commutative`
12×	`frac-times` `times-frac`
11×	`associate-/l/`
10×	`associate-/r/`
9×	`associate-l`
7×	`associate-/l*`
6×	`flip3-+` `flip-+` `div-inv`
4×	`associate-/r*`
2×	`distribute-rgt-out--` `frac-2neg` `distribute-frac-neg` `clear-num` `distribute-lft-out--`
1×	`pow2` `pow-to-exp` `neg-mul-1` `sub-neg` `flip3--` `unpow3` `associate-r` `pow-exp` `prod-exp` `sum-cubes` `distribute-rgt-neg-out` `flip--` `sqr-pow`

Counts

4 → 89

Calls

4 calls:

3.0ms	(* (exp x) (exp x))
2.0ms	(pow (exp x) 3)
20.0ms	(/ (/ (* (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (- y)) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))) (* (* -2 x) z))
10.0ms	(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (exp x) (exp x))
23.0ms	(pow (exp x) 3)
321.0ms	(/ (/ (* (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (- y)) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))) (* (* -2 x) z))
49.0ms	(- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x))))

simplify92.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	689	1418
1	3106	1104
2	5002	1071

prune279.0ms

Filtered

101 candidates to 48 candidates (47.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	101	5	106

Merged error: 0.0b

Counts

106 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) (exp (- x))) (- y)) z)
0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) (- y))
6.3b	(/ (/ (* (+ (exp x) (exp (- x))) (- y)) z) (* -2 x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-/l/`
7×	`associate-/l*`
6×	`associate-*l/`
5×	`*-commutative` `div-inv`
4×	`flip3-+` `flip-+`
3×	`neg-mul-1` `frac-2neg` `distribute-frac-neg` `associate-r` `clear-num` `distribute-rgt-neg-out`
2×	`times-frac` `associate-/r*`
1×	`+-commutative`

Counts

4 → 34

Calls

4 calls:

6.0ms	(/ (* (+ (exp x) (exp (- x))) (- y)) z)
3.0ms	(+ (exp x) (exp (- x)))
4.0ms	(* (+ (exp x) (exp (- x))) (- y))
8.0ms	(/ (/ (* (+ (exp x) (exp (- x))) (- y)) z) (* -2 x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (* (+ (exp x) (exp (- x))) (- y)) z)
23.0ms	(+ (exp x) (exp (- x)))
56.0ms	(* (+ (exp x) (exp (- x))) (- y))
94.0ms	(/ (/ (* (+ (exp x) (exp (- x))) (- y)) z) (* -2 x))

simplify40.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	300	288
1	1114	270
2	5002	265

prune139.0ms

Filtered

46 candidates to 40 candidates (87.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	46	5	51

Merged error: 0.0b

Counts

51 → 5

regimes114.0ms

Accuracy

95.8% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.8b

bsearch98.0ms

Steps

Iters	Range		Point
8	1.2354083816328747e-12	3.3027572769117817e-09	1.8559816678073198e-09
9	-1.1053968796375665e-23	-6.907514097030448e-31	-1.7239256270070378e-25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	39
1	60	39
2	74	39
3	74	39

end0.0ms

sample1.0s

Algorithm

intervals

Results

583.0ms

22188×

body

valid