Details

sample39.0ms

Algorithm

intervals

Results

11.0ms	264×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	8×	body	1280	valid
1.0ms	7×	body	320	valid
1.0ms	10×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.6b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite28.0ms

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:

23.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series253.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(/ (- y z) (- a z))
192.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify2.3s

Counts

70 → 70

Iterations

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

prune496.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.9b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
2.7b	(+ (/ (- t x) (/ (- a z) (- y z))) x)
4.1b	(/ (- t x) (/ (- a z) (- y z)))

rewrite373.0ms

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:

36.0ms	(/ (- a z) (- y z))
234.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
61.0ms	(/ (- t x) (/ (- a z) (- y z)))

series652.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- a z) (- y z))
250.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
322.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify592.0ms

Counts

449 → 449

Iterations

Iter	Nodes
done	5001
1	1165
0	360

prune2.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.9b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
2.7b	(fma (/ 1 1) (/ (- t x) (/ (- a z) (- y z))) x)
4.1b	(/ (- 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`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `div-sub`
1×	`fma-udef`

Counts

3 → 275

Calls

3 calls:

20.0ms	(/ (- a z) (- y z))
0.0ms	(fma (/ 1 1) (/ (- t x) (/ (- a z) (- y z))) x)
67.0ms	(/ (- t x) (/ (- a z) (- y z)))

series575.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (- a z) (- y z))
156.0ms	(fma (/ 1 1) (/ (- t x) (/ (- a z) (- y z))) x)
347.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify677.0ms

Counts

284 → 284

Iterations

Iter	Nodes
done	5000
1	1118
0	350

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.9b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.5b	(/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z)))
10.3b	(fma (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (* (cbrt (- a z)) (cbrt (- a z))) 1)) (/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z))) x)

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

728×	`times-frac`
603×	`add-sqr-sqrt` `*-un-lft-identity`
470×	`cbrt-prod`
271×	`add-cube-cbrt`
166×	`distribute-lft-out--` `difference-of-squares`
46×	`associate-/r*`
19×	`associate-/r/`
12×	`flip3--` `flip--`
10×	`div-inv`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`cbrt-div` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`pow1/3` `associate-/l/`
1×	`clear-num` `frac-2neg` `fma-udef`

Counts

4 → 485

Calls

4 calls:

6.0ms	(cbrt (- t x))
7.0ms	(cbrt (- t x))
52.0ms	(/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z)))
5.0ms	(fma (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (* (cbrt (- a z)) (cbrt (- a z))) 1)) (/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z))) x)

series1.5s

Counts

4 → 12

Calls

4 calls:

236.0ms	(cbrt (- t x))
179.0ms	(cbrt (- t x))
225.0ms	(/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z)))
830.0ms	(fma (/ (* (cbrt (- t x)) (cbrt (- t x))) (/ (* (cbrt (- a z)) (cbrt (- a z))) 1)) (/ (cbrt (- t x)) (/ (cbrt (- a z)) (- y z))) x)

simplify969.0ms

Counts

497 → 497

Iterations

Iter	Nodes
done	5000
1	1765
0	666

prune3.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.9b

regimes871.0ms

Accuracy

18.7% (6.5b remaining)

Error of 10.2b against oracle of 3.7b and baseline of 11.7b

bsearch117.0ms

Steps

Iters	Range		Point
5	9.657462100703732e-164	2.2403175115732038e-163	1.630081040842039e-163
8	-7.039674671700918e-71	-6.993920488520829e-74	-1.978277154611088e-73

simplify9.0ms

Iterations

Iter	Nodes
done	40
1	40
0	36

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.1s	7739×	body	80	valid
146.0ms	474×	body	640	valid
116.0ms	282×	body	1280	valid
71.0ms	413×	body	320	valid
32.0ms	269×	body	160	valid
6.0ms	17×	body	2560	valid