Details

sample25.0ms

Algorithm

intervals

Results

11.0ms	260×	body	80	valid
1.0ms	5×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	1280	valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	54	8
1	146	7
2	337	7
3	1017	7
4	3659	7
5	5001	7

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 2.0b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (tanh (/ t y)) (tanh (/ x y)))
0.0b	(tanh (/ x y))
0.9b	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
18×	`frac-sub`
13×	`tanh-def`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
6×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `associate-l`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
2.0ms	(tanh (/ x y))
1.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
11.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

series773.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
83.0ms	(tanh (/ x y))
252.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
213.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

simplify76.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	560	1798
1	2257	1400
2	5001	1397

prune321.0ms

Filtered

126 candidates to 87 candidates (69.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	124	4	128

Merged error: 0.2b

Counts

128 → 4

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(tanh (/ x y))
0.0b	(- (tanh (/ t y)) (tanh (/ x y)))
5.3b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt` `*-un-lft-identity` `prod-diff`
23×	`add-cube-cbrt`
18×	`frac-sub`
13×	`tanh-def`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`flip3--` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `associate-l` `*-commutative`

Counts

3 → 104

Calls

3 calls:

2.0ms	(tanh (/ x y))
7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
12.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

series473.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(tanh (/ x y))
227.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
163.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	647	1771
1	2868	1370
2	5001	1367

prune254.0ms

Filtered

113 candidates to 72 candidates (63.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	112	5	117

Merged error: 0.2b

Counts

117 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))
7.3b	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
7.3b	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
7.3b	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
36×	`frac-sub`
33×	`cbrt-div`
24×	`tanh-def`
19×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg`
1×	`associate-l` `*-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

14.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))
14.0ms	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
10.0ms	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
10.0ms	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (* y z) (- (tanh (/ t y)) (tanh (/ x y))))
379.0ms	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
378.0ms	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))
380.0ms	(cbrt (* (* y z) (- (tanh (/ t y)) (tanh (/ x y)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	702	2559
1	2875	2235
2	5001	2217

prune497.0ms

Filtered

133 candidates to 101 candidates (75.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	133	5	138

Merged error: 0.2b

Counts

138 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
5.0b	(sqrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
5.0b	(sqrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

44×	`associate-*r/`
40×	`add-sqr-sqrt`
36×	`*-un-lft-identity` `prod-diff` `frac-sub`
32×	`add-cube-cbrt`
24×	`tanh-def`
22×	`distribute-rgt-in` `distribute-lft-in` `sqrt-div`
14×	`pow1`
10×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `sqrt-pow1` `pow-prod-down` `flip--` `log1p-expm1-u` `add-log-exp`
2×	`pow1/2` `prod-exp` `sqrt-prod` `*-commutative` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 158

Calls

4 calls:

15.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
11.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
11.0ms	(sqrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
12.0ms	(sqrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))

series2.7s

Counts

4 → 12

Calls

4 calls:

210.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
370.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
1.1s	(sqrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
1.1s	(sqrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	585	2838
1	2324	2306
2	5002	2300

prune505.0ms

Filtered

170 candidates to 112 candidates (65.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	170	5	175

Merged error: 0.2b

Counts

175 → 5

regimes143.0ms

Accuracy

40.4% (2.4b remaining)

Error of 2.8b against oracle of 0.4b and baseline of 4.4b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample614.0ms

Algorithm

intervals

Results

340.0ms	8277×	body	80	valid
18.0ms	118×	body	640	valid
9.0ms	41×	body	1280	valid
8.0ms	66×	body	320	valid
3.0ms	39×	body	160	valid