Details

sample24.0ms

Algorithm

intervals

Results

11.0ms	263×	body	80	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	640	valid
0.0ms	2×	body	1280	valid
0.0ms	3×	body	160	valid

simplify81.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	8
1	141	8
2	325	8
3	964	8
4	3472	8
5	5002	8

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: 3.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
0.0b	(tanh (/ t y))
0.2b	(- (tanh (/ t y)) (tanh (/ x y)))
4.1b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`frac-sub`
13×	`tanh-def`
11×	`associate-*r/`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in`
2×	`flip3--` `associate-l` `*-commutative` `flip--`
1×	`+-commutative` `flip3-+` `flip-+`

Counts

4 → 41

Calls

4 calls:

8.0ms	(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
2.0ms	(tanh (/ t y))
5.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
8.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series774.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(+ x (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
78.0ms	(tanh (/ t y))
219.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
153.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify54.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	457	759
1	1801	759
2	5001	759

prune181.0ms

Filtered

53 candidates to 42 candidates (79.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	46	7	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 0.3b

Counts

54 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* z (* y (- (tanh (/ t y)) (tanh (/ x y)))))
0.0b	(tanh (/ t y))
0.2b	(- (tanh (/ t y)) (tanh (/ x y)))
1.6b	(* y (- (tanh (/ t y)) (tanh (/ x y))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`associate-*r/`
27×	`frac-sub`
19×	`tanh-def`
10×	`distribute-rgt-in` `distribute-lft-in`
7×	`sub-neg`
3×	`flip3--` `*-commutative` `flip--`
2×	`associate-r`

Counts

4 → 54

Calls

4 calls:

8.0ms	(* z (* y (- (tanh (/ t y)) (tanh (/ x y)))))
2.0ms	(tanh (/ t y))
5.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
7.0ms	(* y (- (tanh (/ t y)) (tanh (/ x y))))

series649.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(* z (* y (- (tanh (/ t y)) (tanh (/ x y)))))
79.0ms	(tanh (/ t y))
216.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
160.0ms	(* y (- (tanh (/ t y)) (tanh (/ x y))))

simplify47.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	409	952
1	1506	952
2	5002	952

prune215.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	64	2	66
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.2b

Counts

73 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))
1.7b	(* z (* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))))
1.8b	(* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
9.8b	(/ (* z (* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

6780×	`frac-add`
6093×	`frac-times`
5416×	`tanh-def`
3407×	`associate-/r/`
2041×	`associate-*r/`
2031×	`associate-*l/`
16×	`flip3-+` `flip-+`
14×	`associate-r`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`sqr-pow`
7×	`sub-neg`
6×	`associate-/l*`
5×	`*-commutative`
4×	`difference-cubes` `flip3--` `flip--` `difference-of-squares`
2×	`associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

4 → 3448

Calls

4 calls:

4.0ms	(- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))
7.0ms	(* z (* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))))
5.0ms	(* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
291.0ms	(/ (* z (* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

series19.3s

Counts

4 → 12

Calls

4 calls:

1.0s	(- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))
887.0ms	(* z (* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3))))
281.0ms	(* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))
17.1s	(/ (* z (* y (- (pow (tanh (/ t y)) 3) (pow (tanh (/ x y)) 3)))) (+ (* (tanh (/ t y)) (tanh (/ t y))) (+ (* (tanh (/ x y)) (tanh (/ x y))) (* (tanh (/ t y)) (tanh (/ x y))))))

simplify2.3s

Algorithm

egg-herbie

Counts

3460 → 3460

Iterations

Useful iterations: 0 (174.0ms)

Iter	Nodes	Cost
0	13266	290179

prune36.9s

Filtered

3460 candidates to 3447 candidates (99.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	3460	0	3460
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	3460	3	3463

Merged error: 0.2b

Counts

3463 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (tanh (/ t y)) (tanh (/ t y)))
0.2b	(- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y))))
4.2b	(/ (* (* y z) (- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y))))) (+ (tanh (/ t y)) (tanh (/ x y))))
5.3b	(* (* y z) (- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y)))))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

819×	`frac-times`
734×	`tanh-def`
727×	`associate-*r/`
675×	`frac-sub`
273×	`associate-*l/`
227×	`associate-/l/`
17×	`*-commutative`
12×	`difference-of-squares`
11×	`associate-/r/`
9×	`frac-add`
8×	`associate-r` `associate-/l*`
4×	`associate-l`
3×	`sub-neg` `flip3--` `flip--`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`pow2` `frac-2neg` `flip3-+` `clear-num` `flip-+` `div-inv`

Counts

4 → 737

Calls

4 calls:

5.0ms	(* (tanh (/ t y)) (tanh (/ t y)))
20.0ms	(- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y))))
59.0ms	(/ (* (* y z) (- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y))))) (+ (tanh (/ t y)) (tanh (/ x y))))
45.0ms	(* (* y z) (- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (tanh (/ t y)) (tanh (/ t y)))
489.0ms	(- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y))))
1.0s	(/ (* (* y z) (- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y))))) (+ (tanh (/ t y)) (tanh (/ x y))))
270.0ms	(* (* y z) (- (* (tanh (/ t y)) (tanh (/ t y))) (* (tanh (/ x y)) (tanh (/ x y)))))

simplify278.0ms

Algorithm

egg-herbie

Counts

749 → 749

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4907	27546
1	5001	27546

prune3.5s

Filtered

749 candidates to 498 candidates (66.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	749	0	749
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	749	3	752

Merged error: 0.2b

Counts

752 → 3

regimes146.0ms

Accuracy

53.6% (5.3b remaining)

Error of 5.4b against oracle of 0.0b and baseline of 11.5b

bsearch105.0ms

Steps

Iters	Range		Point
8	1.2824227115956784e+127	3.40936178854925e+129	1.6057920252528938e+127
8	-6.189426906258438e+158	-1.4497606012047558e+156	-2.14779953698364e+156

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	31
1	41	31

end0.0ms

sample606.0ms

Algorithm

intervals

Results

344.0ms	8278×	body	80	valid
14.0ms	92×	body	640	valid
9.0ms	39×	body	1280	valid
8.0ms	74×	body	320	valid
3.0ms	35×	body	160	valid