Details

sample50.0ms

Algorithm

intervals

Results

16.0ms	243×	body	80	valid
4.0ms	19×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	7×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3818
5	978
4	326
3	116
2	45
1	20
0	11

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize27.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.0b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite40.0ms

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:

36.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series268.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(/ (- y z) (- a z))
199.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify2.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
3	4622
2	860
1	271
0	116

prune476.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.1b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
1.3b	(/ (- t x) (/ (- a z) (- y z)))
2.7b	(+ (/ (- t x) (/ (- a z) (- y z))) x)

rewrite284.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `div-inv` `flip--`
10×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `associate-+l-` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

21.0ms	(/ (- a z) (- y z))
31.0ms	(/ (- t x) (/ (- a z) (- y z)))
192.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

series549.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (- a z) (- y z))
265.0ms	(/ (- t x) (/ (- a z) (- y z)))
227.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

simplify645.0ms

Counts

449 → 449

Iterations

Iter	Nodes
done	5000
1	1165
0	360

prune2.4s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 3.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
4.7b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-/r` `associate-l*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 105

Calls

3 calls:

19.0ms	(/ 1 (- a z))
68.0ms	(* (- y z) (/ 1 (- a z)))
1.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series420.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ 1 (- a z))
116.0ms	(* (- y z) (/ 1 (- a z)))
230.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify4.1s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	2819
1	363
0	152

prune701.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 3.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt (- a z))
9.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
0.0ms	(fma (/ 1 (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- y z)) (cbrt (- y z))))) (/ (- t x) (/ (cbrt (- a z)) (cbrt (- y z)))) x)

series18.0s

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (- a z))
214.0ms	(cbrt (- a z))
232.0ms	(cbrt (- a z))
17.3s	(fma (/ 1 (/ (* (cbrt (- a z)) (cbrt (- a z))) (* (cbrt (- y z)) (cbrt (- y z))))) (/ (- t x) (/ (cbrt (- a z)) (cbrt (- y z)))) x)

simplify1.7s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
3	4040
2	911
1	312
0	132

prune676.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 3.1b

regimes913.0ms

Accuracy

22.5% (6.1b remaining)

Error of 9.7b against oracle of 3.6b and baseline of 11.5b

bsearch124.0ms

Steps

Iters	Range		Point
9	6.906315603593477e-164	4.557376285322506e-157	1.35258502937208e-160
8	-8.778032766378265e-192	-1.9835161528811826e-194	-2.735236830308559e-193

simplify3.0ms

Iterations

Iter	Nodes
done	28
1	28
0	22

end0.0ms

sample1.8s

Algorithm

intervals

Results

749.0ms	7819×	body	80	valid
160.0ms	402×	body	320	valid
110.0ms	479×	body	640	valid
83.0ms	272×	body	1280	valid
30.0ms	258×	body	160	valid
5.0ms	16×	body	2560	valid