Details

sample40.0ms

Algorithm

intervals

Results

24.0ms	263×	body	80	valid
1.0ms	5×	body	640	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	12	15
1	54	15
2	147	14
3	334	14
4	996	14
5	3305	14
done	5000	14

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (tanh (/ t y)) (tanh (/ x y)))
0.0b	(tanh (/ x y))
0.6b	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
1.5b	(* z (- (tanh (/ t y)) (tanh (/ x y))))

rewrite133.0ms

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:

27.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
4.0ms	(tanh (/ x y))
1.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
92.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

series1.5s

Counts

4 → 12

Calls

4 calls:

300.0ms	(- (tanh (/ t y)) (tanh (/ x y)))
115.0ms	(tanh (/ x y))
384.0ms	(fma y (* z (- (tanh (/ t y)) (tanh (/ x y)))) x)
697.0ms	(* z (- (tanh (/ t y)) (tanh (/ x y))))

simplify1.3s

Counts

126 → 126

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	221	3259
1	561	2726
2	1841	2366
done	5000	2137

prune628.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(tanh (/ x y))
0.6b	(fma y (+ (* (tanh (/ t y)) z) (* (- (tanh (/ x y))) z)) x)
2.0b	(* (tanh (/ t y)) z)
2.8b	(* (- (tanh (/ x y))) z)

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-*l/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `distribute-neg-frac` `tanh-def`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-lft-neg-out` `neg-mul-1` `fma-udef`

Counts

4 → 76

Calls

4 calls:

4.0ms	(tanh (/ x y))
1.0ms	(fma y (+ (* (tanh (/ t y)) z) (* (- (tanh (/ x y))) z)) x)
24.0ms	(* (tanh (/ t y)) z)
30.0ms	(* (- (tanh (/ x y))) z)

series835.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(tanh (/ x y))
378.0ms	(fma y (+ (* (tanh (/ t y)) z) (* (- (tanh (/ x y))) z)) x)
177.0ms	(* (tanh (/ t y)) z)
174.0ms	(* (- (tanh (/ x y))) z)

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	146	953
1	340	911
2	1146	814
done	5001	809

prune417.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

2.8b	(* (- (* (* (cbrt (tanh (/ x y))) (cbrt (tanh (/ x y)))) (cbrt (tanh (/ x y))))) z)
5.9b	(cbrt (tanh (/ x y)))
5.9b	(cbrt (tanh (/ x y)))
5.9b	(cbrt (tanh (/ x y)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

153×	`cbrt-div`
90×	`associate-*l/`
81×	`frac-times`
63×	`distribute-neg-frac`
51×	`tanh-def`
15×	`associate-*r/`
11×	`add-sqr-sqrt`
9×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r`
1×	`distribute-lft-neg-out` `distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 135

Calls

4 calls:

147.0ms	(* (- (* (* (cbrt (tanh (/ x y))) (cbrt (tanh (/ x y)))) (cbrt (tanh (/ x y))))) z)
3.0ms	(cbrt (tanh (/ x y)))
2.0ms	(cbrt (tanh (/ x y)))
3.0ms	(cbrt (tanh (/ x y)))

series822.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (- (* (* (cbrt (tanh (/ x y))) (cbrt (tanh (/ x y)))) (cbrt (tanh (/ x y))))) z)
264.0ms	(cbrt (tanh (/ x y)))
199.0ms	(cbrt (tanh (/ x y)))
220.0ms	(cbrt (tanh (/ x y)))

simplify1.8s

Counts

147 → 147

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	319	3270
1	826	3140
2	1830	2750
done	5000	2642

prune1.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize51.0ms

Local error

Found 4 expressions with local error:

5.9b	(cbrt (tanh (/ x y)))
5.9b	(cbrt (tanh (/ x y)))
5.9b	(cbrt (tanh (/ x y)))
5.9b	(cbrt (tanh (/ x y)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod` `cbrt-div`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `tanh-def` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

3.0ms	(cbrt (tanh (/ x y)))
2.0ms	(cbrt (tanh (/ x y)))
3.0ms	(cbrt (tanh (/ x y)))
3.0ms	(cbrt (tanh (/ x y)))

series1.1s

Counts

4 → 12

Calls

4 calls:

283.0ms	(cbrt (tanh (/ x y)))
279.0ms	(cbrt (tanh (/ x y)))
257.0ms	(cbrt (tanh (/ x y)))
261.0ms	(cbrt (tanh (/ x y)))

simplify2.9s

Counts

76 → 76

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	70	964
1	149	928
2	323	888
3	990	848
4	4207	768
done	5001	764

prune569.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

regimes259.0ms

Accuracy

0% (1.8b remaining)

Error of 2.3b against oracle of 0.4b and baseline of 2.3b

bsearch0.0ms

simplify17.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	45
1	30	45
2	45	45
3	48	45
done	48	45

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.4s	8312×	body	80	valid
36.0ms	98×	body	640	valid
22.0ms	49×	body	1280	valid
16.0ms	61×	body	320	valid
5.0ms	31×	body	160	valid