Details

sample64.0ms

Algorithm

intervals

Results

24.0ms	251×	body	80	valid
3.0ms	13×	body	640	valid
3.0ms	13×	body	320	valid
3.0ms	7×	body	1280	valid
1.0ms	8×	body	160	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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize34.0ms

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))

rewrite137.0ms

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:

50.0ms	(* (- y z) (- t x))
32.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
52.0ms	(/ (* (- y z) (- t x)) (- a z))

series467.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* (- y z) (- t x))
233.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
187.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify1.6s

Counts

90 → 90

Iterations

Iter	Nodes
done	5012
2	1852
1	478
0	162

prune702.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

localize55.0ms

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)))))

rewrite186.0ms

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:

6.0ms	(cbrt (- a z))
6.0ms	(cbrt (- a z))
155.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (- a z))
220.0ms	(cbrt (- a z))
419.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
237.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify3.2s

Counts

146 → 146

Iterations

Iter	Nodes
done	5002
2	2899
1	745
0	255

prune979.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.1b

localize21.0ms

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)))

rewrite91.0ms

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))
9.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
60.0ms	(* (- y z) (/ (- t x) (- a z)))

series509.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- t x) (- a z))
235.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
201.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.6s

Counts

128 → 128

Iterations

Iter	Nodes
done	5001
2	1764
1	500
0	183

prune700.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

localize25.0ms

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)))

rewrite194.0ms

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:

31.0ms	(/ (- a z) (- t x))
84.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
50.0ms	(/ (- y z) (/ (- a z) (- t x)))

series700.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- a z) (- t x))
264.0ms	(+ x (/ (- y z) (/ (- a z) (- t x))))
363.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify2.2s

Counts

283 → 283

Iterations

Iter	Nodes
done	5001
2	3704
1	1143
0	352

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.1b

regimes664.0ms

Accuracy

30.8% (5.9b remaining)

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

bsearch95.0ms

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

613.0ms	7813×	body	80	valid
91.0ms	484×	body	640	valid
59.0ms	252×	body	1280	valid
57.0ms	413×	body	320	valid
46.0ms	253×	body	160	valid
6.0ms	20×	body	2560	valid