Details

analyze808.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
7.8%	92%	0.2%	8
7.8%	92%	0.2%	9
10.9%	88.9%	0.2%	10
34.7%	65.1%	0.2%	11
43.1%	56.7%	0.2%	12
44.2%	55.7%	0.2%	13
49.5%	50.3%	0.2%	14

sample26.0ms

Algorithm

intervals

Results

12.0ms	252×	body	80	valid
1.0ms	23×	body	80	invalid
0.0ms	2×	body	640	valid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5059	15

prune16.0ms

Filtered

1 candidates to 1 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: 1.6b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ x y))
0.3b	(- (tanh (/ t y)) (tanh (/ x y)))
1.1b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
3.5b	(* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`associate-*r/`
27×	`frac-sub`
19×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
13×	`add-sqr-sqrt`
11×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
7×	`add-cube-cbrt` `sub-neg`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`flip3--` `flip--`
2×	`*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

2.0ms	(tanh (/ x y))
7.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
9.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
11.0ms	(* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))

series257.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(tanh (/ x y))
74.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
88.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
68.0ms	(* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))

simplify35.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4987	2251
1	4987	2251

prune179.0ms

Filtered

85 candidates to 110 candidates (-29.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	105	7	112

Merged error: 1.6b

Counts

112 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y)))))
1.5b	(* z (neg (tanh (/ x y))))
2.2b	(* z (tanh (/ t y)))
3.5b	(* y (+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

53×	`associate-*r/`
21×	`distribute-neg-frac`
18×	`add-sqr-sqrt` `frac-add`
17×	`associate-r`
14×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-l`
6×	`add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `distribute-rgt-neg-out` `flip-+` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `neg-mul-1` `distribute-lft-in` `unsub-neg` `sum-log`

Counts

4 → 104

Calls

4 calls:

8.0ms	(+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y)))))
6.0ms	(* z (neg (tanh (/ x y))))
5.0ms	(* z (tanh (/ t y)))
10.0ms	(* y (+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y))))))

series221.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y)))))
34.0ms	(* z (neg (tanh (/ x y))))
31.0ms	(* z (tanh (/ t y)))
73.0ms	(* y (+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4969	1909
1	4969	1909

prune156.0ms

Filtered

91 candidates to 116 candidates (-27.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	117	6	123

Merged error: 1.6b

Counts

123 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b	(* z (tanh (/ t y)))
5.1b	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
5.1b	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
5.1b	(cbrt (+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y))))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

43×	`associate-*r/`
33×	`cbrt-div`
19×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
18×	`frac-sub`
9×	`add-sqr-sqrt` `frac-add` `distribute-neg-frac`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`flip3--` `flip--`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

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

series672.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* z (tanh (/ t y)))
220.0ms	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
215.0ms	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
205.0ms	(cbrt (+ (* z (tanh (/ t y))) (* z (neg (tanh (/ x y))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5156	2888

prune210.0ms

Filtered

88 candidates to 96 candidates (-9.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	96	6	102

Merged error: 1.6b

Counts

102 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

1.7b	(* y (* (cbrt (* z (- (tanh (/ t y)) (tanh (/ x y))))) (cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))))
3.5b	(cbrt (- (tanh (/ t y)) (tanh (/ x y))))
5.1b	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
5.1b	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

440×	`associate-*r/`
297×	`cbrt-div`
243×	`frac-sub`
162×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
121×	`frac-times`
27×	`flip3--` `flip--`
11×	`associate-*l/`
9×	`pow1` `add-exp-log` `add-sqr-sqrt`
8×	`*-un-lft-identity`
7×	`cbrt-prod` `add-cbrt-cube`
6×	`add-cube-cbrt`
4×	`add-log-exp`
3×	`pow1/3` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`associate-r` `*-commutative` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 226

Calls

4 calls:

27.0ms	(* y (* (cbrt (* z (- (tanh (/ t y)) (tanh (/ x y))))) (cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))))
7.0ms	(cbrt (- (tanh (/ t y)) (tanh (/ x y))))
11.0ms	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
8.0ms	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))

series830.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(* y (* (cbrt (* z (- (tanh (/ t y)) (tanh (/ x y))))) (cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))))
143.0ms	(cbrt (- (tanh (/ t y)) (tanh (/ x y))))
215.0ms	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))
211.0ms	(cbrt (* z (- (tanh (/ t y)) (tanh (/ x y)))))

simplify101.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5192	13557

prune886.0ms

Filtered

216 candidates to 238 candidates (-10.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	238	0	238
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	238	6	244

Merged error: 1.6b

Counts

244 → 6

regimes355.0ms

Accuracy

0% (0.6b remaining)

Error of 2.2b against oracle of 1.6b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	17
1	43	17

end0.0ms

sample661.0ms

Algorithm

intervals

Results

377.0ms	7764×	body	80	valid
29.0ms	555×	body	80	invalid
17.0ms	93×	body	640	valid
11.0ms	44×	body	1280	valid
8.0ms	56×	body	320	valid
4.0ms	43×	body	160	valid

Details

analyze808.0ms

sample26.0ms

simplify29.0ms

prune16.0ms

localize11.0ms

rewrite33.0ms

series257.0ms

simplify35.0ms

prune179.0ms

localize12.0ms

rewrite32.0ms

series221.0ms

simplify51.0ms

prune156.0ms

localize21.0ms

rewrite32.0ms

series672.0ms

simplify43.0ms

prune210.0ms

localize19.0ms

rewrite84.0ms

series830.0ms

simplify101.0ms

prune886.0ms

regimes355.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample661.0ms

Profiling