Details

sample37.0ms

Algorithm

intervals

Results

16.0ms	250×	body	80	valid
2.0ms	10×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	4×	body	1280	valid
1.0ms	6×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1910
5	805
4	299
3	108
2	43
1	20
0	11

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.8b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite46.0ms

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/` `insert-posit16` `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 → 66

Calls

2 calls:

42.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series238.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(/ (- t x) (- a z))
150.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.6s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	2212
2	671
1	276
0	120

prune414.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
11.8b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite71.0ms

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` `insert-posit16` `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 → 108

Calls

3 calls:

13.0ms	(/ 1 (- a z))
55.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series253.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(/ 1 (- a z))
68.0ms	(* (- t x) (/ 1 (- a z)))
132.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify2.4s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4059
2	1322
1	373
0	158

prune690.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.7b	(/ 1 (/ (- a z) (- t x)))
11.8b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
195×	`add-sqr-sqrt` `*-un-lft-identity`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
16×	`add-exp-log`
11×	`associate-/r/`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`flip3--` `div-inv` `flip--`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-/l/`
1×	`div-sub` `fma-udef` `pow-flip` `inv-pow`

Counts

3 → 217

Calls

3 calls:

25.0ms	(/ (- a z) (- t x))
43.0ms	(/ 1 (/ (- a z) (- t x)))
0.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series579.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- a z) (- t x))
307.0ms	(/ 1 (/ (- a z) (- t x)))
192.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify2.1s

Counts

226 → 226

Iterations

Iter	Nodes
done	5003
2	2171
1	713
0	277

prune934.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
11.7b	(fma (* (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (/ 1 (cbrt (- a z)))) (- y z) x)

rewrite24.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 65

Calls

4 calls:

8.0ms	(cbrt (- a z))
8.0ms	(cbrt (- a z))
5.0ms	(cbrt (- a z))
0.0ms	(fma (* (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (/ 1 (cbrt (- a z)))) (- y z) x)

series1.3s

Counts

4 → 12

Calls

4 calls:

255.0ms	(cbrt (- a z))
635.0ms	(cbrt (- a z))
266.0ms	(cbrt (- a z))
157.0ms	(fma (* (/ (/ (- t x) (cbrt (- a z))) (cbrt (- a z))) (/ 1 (cbrt (- a z)))) (- y z) x)

simplify1.8s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
3	1330
2	463
1	207
0	100

prune654.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 5.1b

regimes874.0ms

Accuracy

-2.7% (8.3b remaining)

Error of 14.8b against oracle of 6.6b and baseline of 14.6b

bsearch153.0ms

Steps

Iters	Range		Point
7	1.5715419632280842e-168	2.6109616469994367e-167	1.6219312397286576e-168
8	1.1044943062804207e-253	5.889411553771999e-251	1.285655334612926e-253

simplify7.0ms

Iterations

Iter	Nodes
done	29
1	29
0	21

end0.0ms

sample1.5s

Algorithm

intervals

Results

753.0ms	7809×	body	80	valid
160.0ms	463×	body	640	valid
155.0ms	284×	body	1280	valid
82.0ms	412×	body	320	valid
33.0ms	251×	body	160	valid
5.0ms	11×	body	2560	valid