Details

sample41.0ms

Algorithm

intervals

Results

13.0ms	251×	body	80	valid
4.0ms	8×	body	160	valid
2.0ms	13×	body	640	valid
2.0ms	7×	body	1280	valid
2.0ms	13×	body	320	valid
0.0ms	1×	body	2560	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1620
5	661
4	266
3	103
2	43
1	20
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.9b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.1b	(/ (* (- y z) (- t x)) (- a z))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-cbrt-cube` `add-exp-log`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `associate-/r` `times-frac` `associate-r` `associate-l*` `add-log-exp`
4×	`associate-l/` `associate-r/` `distribute-lft-out--` `difference-of-squares`
2×	`distribute-rgt-in` `cbrt-undiv` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `pow-prod-down` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

29.0ms	(* (- y z) (- t x))
32.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
37.0ms	(/ (* (- y z) (- t x)) (- a z))

series571.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(* (- y z) (- t x))
288.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
222.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5012
2	1852
1	478
0	162

prune720.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-l/` `associate-r/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `sum-log` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
161.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
11.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

197.0ms	(cbrt (- a z))
219.0ms	(cbrt (- a z))
471.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
245.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify2.9s

Counts

146 → 146

Iterations

Iter	Nodes
done	5002
2	2899
1	745
0	255

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.1b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.1b	(* (- y z) (/ (- t x) (- a z)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
2×	`frac-times` `cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `associate-/l/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `flip-+`

Counts

3 → 119

Calls

3 calls:

17.0ms	(/ (- t x) (- a z))
8.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
69.0ms	(* (- y z) (/ (- t x) (- a z)))

series543.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- t x) (- a z))
243.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
221.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.3s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1764
1	500
0	183

prune782.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
2.1b	(+ x (/ (- y z) (/ (- a z) (- t x))))
5.2b	(/ (- y z) (/ (- a z) (- t x)))

rewrite211.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `associate-+r-` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

27.0ms	(/ (- a z) (- t x))
108.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
47.0ms	(/ (- y z) (/ (- a z) (- t x)))

series679.0ms

Counts

3 → 9

Calls

3 calls:

74.0ms	(/ (- a z) (- t x))
189.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
415.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify2.2s

Counts

283 → 283

Iterations

Iter	Nodes
done	5001
2	3704
1	1143
0	352

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

regimes573.0ms

Accuracy

30.8% (5.9b remaining)

Error of 9.0b against oracle of 3.1b and baseline of 11.6b

bsearch90.0ms

Steps

Iters	Range		Point
5	1.4442466631373857e-87	4.390816705502575e-87	2.1779022340014837e-87
6	-1.1682718823344e-108	-2.48590275519429e-109	-2.669212786079051e-109

simplify6.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample1.5s

Algorithm

intervals

Results

846.0ms	7813×	body	80	valid
88.0ms	484×	body	640	valid
87.0ms	252×	body	1280	valid
55.0ms	413×	body	320	valid
22.0ms	253×	body	160	valid
5.0ms	20×	body	2560	valid