Details

sample47.0ms

Algorithm

intervals

Results

13.0ms	250×	body	80	valid
4.0ms	16×	body	1280	valid
3.0ms	15×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	5×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	3252
5	844
4	292
3	111
2	45
1	20
0	11

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.4b	(+ x (* (/ (- y z) (- a z)) (- t x)))
2.0b	(* (/ (- y z) (- a z)) (- t x))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

29.0ms	(/ (- y z) (- a z))
10.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))
67.0ms	(* (/ (- y z) (- a z)) (- t x))

series662.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (- y z) (- a z))
205.0ms	(+ x (* (/ (- y z) (- a z)) (- t x)))
403.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify1.0s

Counts

136 → 136

Iterations

Iter	Nodes
done	5001
2	2148
1	536
0	195

prune704.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.6b	(/ 1 (/ (- a z) (- y z)))
1.4b	(+ x (* (/ 1 (/ (- a z) (- y z))) (- t x)))
2.0b	(* (/ 1 (/ (- a z) (- y z))) (- t x))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-l`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*` `add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-r` `unswap-sqr`
4×	`distribute-rgt-in` `rec-exp` `associate-+r+` `sub-neg` `distribute-lft-in` `1-exp`
3×	`cbrt-unprod`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*r/` `associate-/l/`
1×	`+-commutative` `sum-log` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 351

Calls

4 calls:

17.0ms	(/ (- a z) (- y z))
24.0ms	(/ 1 (/ (- a z) (- y z)))
6.0ms	(+ x (* (/ 1 (/ (- a z) (- y z))) (- t x)))
85.0ms	(* (/ 1 (/ (- a z) (- y z))) (- t x))

series877.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (- a z) (- y z))
167.0ms	(/ 1 (/ (- a z) (- y z)))
237.0ms	(+ x (* (/ 1 (/ (- a z) (- y z))) (- t x)))
397.0ms	(* (/ 1 (/ (- a z) (- y z))) (- t x))

simplify563.0ms

Counts

363 → 363

Iterations

Iter	Nodes
done	5000
1	1195
0	401

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
1.4b	(+ x (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (- t x) (/ (- a z) (- y z)))))
2.4b	(/ (- t x) (/ (- a z) (- y z)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
321×	`add-sqr-sqrt` `*-un-lft-identity`
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`
2×	`clear-num` `frac-2neg` `div-sub`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

3 → 272

Calls

3 calls:

25.0ms	(/ (- a z) (- y z))
8.0ms	(+ x (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (- t x) (/ (- a z) (- y z)))))
47.0ms	(/ (- t x) (/ (- a z) (- y z)))

series643.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (- a z) (- y z))
252.0ms	(+ x (* (/ (* (cbrt 1) (cbrt 1)) 1) (/ (- t x) (/ (- a z) (- y z)))))
318.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify525.0ms

Counts

281 → 281

Iterations

Iter	Nodes
done	5000
1	1173
0	359

prune1.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
10.2b	(+ x (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`distribute-rgt-in` `distribute-lft-in`
16×	`associate-+r+`
15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`sub-neg`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 72

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
15.0ms	(+ x (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z)))))

series735.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt (- a z))
174.0ms	(cbrt (- a z))
198.0ms	(cbrt (- a z))
190.0ms	(+ x (* (/ (* (cbrt 1) (cbrt 1)) 1) (* (* (/ (cbrt (- t x)) (cbrt (- a z))) (/ (cbrt (- t x)) (cbrt (- a z)))) (* (/ (cbrt (- t x)) (cbrt (- a z))) (- y z)))))

simplify793.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
2	1393
1	354
0	132

prune664.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.4b

regimes709.0ms

Accuracy

14.6% (6.9b remaining)

Error of 10.7b against oracle of 3.8b and baseline of 11.9b

bsearch122.0ms

Steps

Iters	Range		Point
10	2.1039460058121797e-189	5.334963794456662e-178	5.909250579364138e-179
6	-2.4031652791127273e-20	-2.0990955826697636e-21	-2.1458694787615367e-21

simplify6.0ms

Iterations

Iter	Nodes
done	40
3	40
2	38
1	37
0	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

606.0ms	7893×	body	80	valid
74.0ms	428×	body	640	valid
71.0ms	322×	body	1280	valid
47.0ms	376×	body	320	valid
22.0ms	260×	body	160	valid
5.0ms	19×	body	2560	valid