Details

sample40.0ms

Algorithm

intervals

Results

13.0ms	253×	body	80	valid
3.0ms	14×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	2×	body	2560	valid
1.0ms	5×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3874
5	979
4	326
3	116
2	45
1	20
0	11

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.1b	(fma (/ (- z t) (- a t)) (- y x) x)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log`
2×	`expm1-log1p-u` `pow1` `flip3--` `associate-/r/` `log1p-expm1-u` `flip--` `add-log-exp` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

24.0ms	(/ (- z t) (- a t))
0.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

series251.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(/ (- z t) (- a t))
178.0ms	(fma (/ (- z t) (- a t)) (- y x) x)

simplify1.9s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4602
2	861
1	272
0	116

prune551.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
0.2b	(/ 1 (/ (- a t) (- z t)))
2.1b	(fma (/ 1 (/ (- a t) (- z t))) (- y x) x)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `div-inv` `flip--`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`div-sub` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 214

Calls

3 calls:

29.0ms	(/ (- a t) (- z t))
34.0ms	(/ 1 (/ (- a t) (- z t)))
1.0ms	(fma (/ 1 (/ (- a t) (- z t))) (- y x) x)

series410.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (- a t) (- z t))
168.0ms	(/ 1 (/ (- a t) (- z t)))
176.0ms	(fma (/ 1 (/ (- a t) (- z t))) (- y x) x)

simplify1.8s

Counts

223 → 223

Iterations

Iter	Nodes
done	5002
2	3962
1	714
0	273

prune871.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ a (- z t))
0.0b	(/ t (- z t))
0.2b	(/ 1 (- (/ a (- z t)) (/ t (- z t))))
2.1b	(fma (/ 1 (- (/ a (- z t)) (/ t (- z t)))) (- y x) x)

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

175×	`*-un-lft-identity`
156×	`times-frac`
135×	`add-sqr-sqrt`
56×	`distribute-lft-out--`
55×	`add-cube-cbrt`
32×	`difference-of-squares`
28×	`associate-/r*`
24×	`associate-/r/`
12×	`distribute-rgt-out--` `add-exp-log`
11×	`flip3--` `div-inv` `flip--`
10×	`add-cbrt-cube`
9×	`associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg`
1×	`rec-exp` `1-exp` `frac-sub` `fma-udef` `pow-flip` `inv-pow` `sub-div`

Counts

4 → 185

Calls

4 calls:

12.0ms	(/ a (- z t))
9.0ms	(/ t (- z t))
153.0ms	(/ 1 (- (/ a (- z t)) (/ t (- z t))))
1.0ms	(fma (/ 1 (- (/ a (- z t)) (/ t (- z t)))) (- y x) x)

series388.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ a (- z t))
61.0ms	(/ t (- z t))
126.0ms	(/ 1 (- (/ a (- z t)) (/ t (- z t))))
162.0ms	(fma (/ 1 (- (/ a (- z t)) (/ t (- z t)))) (- y x) x)

simplify1.1s

Counts

197 → 197

Iterations

Iter	Nodes
done	5001
2	2549
1	548
0	275

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

localize65.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.6b	(cbrt t)
0.6b	(cbrt t)
2.8b	(fma (/ 1 (- (/ a (- z t)) (* (* (/ (cbrt t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt t)) (/ (cbrt t) (cbrt (- z t)))))) (- y x) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(cbrt t)
1.0ms	(fma (/ 1 (- (/ a (- z t)) (* (* (/ (cbrt t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt t)) (/ (cbrt t) (cbrt (- z t)))))) (- y x) x)

series958.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(cbrt t)
234.0ms	(cbrt t)
277.0ms	(cbrt t)
199.0ms	(fma (/ 1 (- (/ a (- z t)) (* (* (/ (cbrt t) (* (cbrt (- z t)) (cbrt (- z t)))) (cbrt t)) (/ (cbrt t) (cbrt (- z t)))))) (- y x) x)

simplify735.0ms

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
3	1373
2	305
1	110
0	58

prune528.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.4b

regimes891.0ms

Accuracy

25.8% (6.0b remaining)

Error of 9.6b against oracle of 3.6b and baseline of 11.7b

bsearch206.0ms

Steps

Iters	Range		Point
10	4.5158289857264295e-178	4.753875386860788e-168	1.0211067349911059e-168
7	-1.857850302800927e-158	-1.3110312091667196e-160	-8.572794558051977e-160

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample1.5s

Algorithm

intervals

Results

730.0ms	7915×	body	80	valid
131.0ms	450×	body	640	valid
77.0ms	274×	body	1280	valid
76.0ms	433×	body	320	valid
64.0ms	222×	body	160	valid
6.0ms	15×	body	2560	valid