Details

analyze795.0ms

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

sample25.0ms

Algorithm

intervals

Results

11.0ms	243×	body	80	valid
1.0ms	20×	body	80	invalid
1.0ms	4×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	1280	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5059	15

prune13.0ms

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: 1.7b

Counts

2 → 2

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ x y))
0.0b	(tanh (/ t y))
1.0b	(* z (- (tanh (/ t y)) (tanh (/ x y))))
2.7b	(* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

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

series203.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(tanh (/ x y))
26.0ms	(tanh (/ t y))
85.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))
66.0ms	(* y (* z (- (tanh (/ t y)) (tanh (/ x y)))))

simplify29.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5619	1645

prune158.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 1.7b

Counts

100 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.8b	(* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y))
0.9b	(* z (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y)))
1.6b	(* (* (cbrt y) (cbrt y)) (* z (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

33×	`associate-r/` `associate-l/`
32×	`pow1` `add-exp-log`
27×	`frac-sub`
22×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
18×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt` `associate-l`
8×	`associate-r`
7×	`cbrt-prod`
4×	`add-log-exp`
3×	`flip3--` `*-commutative` `flip--`
2×	`unswap-sqr`
1×	`pow1/3` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

1.0ms	(cbrt y)
11.0ms	(* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y))
12.0ms	(* z (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y)))
17.0ms	(* (* (cbrt y) (cbrt y)) (* z (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y))))

series325.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt y)
115.0ms	(* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y))
118.0ms	(* z (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y)))
71.0ms	(* (* (cbrt y) (cbrt y)) (* z (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt y))))

simplify61.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4980	2399
1	4980	2399

prune184.0ms

Filtered

93 candidates to 126 candidates (-35.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	126	9	135

Merged error: 1.5b

Counts

135 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

2.7b	(* y (* z (- (* (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y)))) (tanh (/ x y)))))
7.3b	(cbrt (tanh (/ t y)))
7.3b	(cbrt (tanh (/ t y)))
7.3b	(cbrt (tanh (/ t y)))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

441×	`cbrt-div`
427×	`associate-*r/`
243×	`frac-times`
210×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
189×	`frac-sub`
81×	`associate-*l/`
9×	`pow1` `add-exp-log` `cbrt-prod` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-log-exp`
3×	`pow1/3` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`flip3--` `associate-r` `*-commutative` `flip--`

Counts

4 → 255

Calls

4 calls:

55.0ms	(* y (* z (- (* (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y)))) (tanh (/ x y)))))
2.0ms	(cbrt (tanh (/ t y)))
2.0ms	(cbrt (tanh (/ t y)))
2.0ms	(cbrt (tanh (/ t y)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* y (* z (- (* (* (cbrt (tanh (/ t y))) (cbrt (tanh (/ t y)))) (cbrt (tanh (/ t y)))) (tanh (/ x y)))))
50.0ms	(cbrt (tanh (/ t y)))
49.0ms	(cbrt (tanh (/ t y)))
56.0ms	(cbrt (tanh (/ t y)))

simplify124.0ms

Algorithm

egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4985	14799
1	4985	14799

prune828.0ms

Filtered

182 candidates to 267 candidates (-46.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	267	0	267
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	267	9	276

Merged error: 1.5b

Counts

276 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
0.6b	(cbrt z)
0.9b	(* (* (cbrt z) (cbrt z)) (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt z)))
2.7b	(* y (* (* (cbrt z) (cbrt z)) (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt z))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

34×	`pow1` `add-exp-log`
33×	`associate-*r/`
22×	`associate-*l/` `add-cbrt-cube`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
18×	`frac-sub`
12×	`tanh-def-c` `tanh-def-b` `tanh-def-a`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
4×	`associate-l` `add-log-exp`
2×	`flip3--` `pow1/3` `associate-r` `*-commutative` `flip--`

Counts

4 → 93

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
15.0ms	(* (* (cbrt z) (cbrt z)) (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt z)))
18.0ms	(* y (* (* (cbrt z) (cbrt z)) (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt z))))

series203.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt z)
21.0ms	(cbrt z)
90.0ms	(* (* (cbrt z) (cbrt z)) (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt z)))
72.0ms	(* y (* (* (cbrt z) (cbrt z)) (* (- (tanh (/ t y)) (tanh (/ x y))) (cbrt z))))

simplify45.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5900	1574

prune101.0ms

Filtered

68 candidates to 105 candidates (-54.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	105	9	114

Merged error: 1.5b

Counts

114 → 9

regimes410.0ms

Accuracy

0% (1.3b remaining)

Error of 2.2b against oracle of 0.9b and baseline of 2.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	15
1	25	15

end0.0ms

sample649.0ms

Algorithm

intervals

Results

368.0ms	7735×	body	80	valid
26.0ms	564×	body	80	invalid
19.0ms	105×	body	640	valid
15.0ms	58×	body	1280	valid
8.0ms	57×	body	320	valid
7.0ms	45×	body	160	valid

Details

analyze795.0ms

sample25.0ms

simplify30.0ms

prune13.0ms

localize15.0ms

rewrite27.0ms

series203.0ms

simplify29.0ms

prune158.0ms

localize17.0ms

rewrite45.0ms

series325.0ms

simplify61.0ms

prune184.0ms

localize15.0ms

rewrite91.0ms

series219.0ms

simplify124.0ms

prune828.0ms

localize18.0ms

rewrite39.0ms

series203.0ms

simplify45.0ms

prune101.0ms

regimes410.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample649.0ms

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