Details

sample57.0ms

Algorithm

intervals

Results

25.0ms

281×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (24.0ms)

Iter	Nodes	Cost
0	10	11
1	17	11
2	35	11
3	63	10
4	106	10
5	167	10
6	222	10
7	255	10
8	289	10
9	338	10
10	450	10
11	570	10
12	624	10
13	636	10
14	638	10
done	638	10

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.7b	(fma (/ (- y z) (- a z)) t x)

rewrite68.0ms

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-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

62.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) t x)

series213.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(/ (- y z) (- a z))
124.0ms	(fma (/ (- y z) (- a z)) t x)

simplify3.4s

Counts

70 → 70

Iterations

Useful iterations: 4 (2.0s)

Iter	Nodes	Cost
0	113	884
1	259	856
2	633	808
3	1589	808
4	4605	806
done	5000	806

prune256.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
1.7b	(fma (* (- y z) (/ 1 (- a z))) t x)

rewrite106.0ms

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-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

23.0ms	(/ 1 (- a z))
78.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) t x)

series286.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ 1 (- a z))
87.0ms	(* (- y z) (/ 1 (- a z)))
127.0ms	(fma (* (- y z) (/ 1 (- a z))) t x)

simplify3.4s

Counts

114 → 114

Iterations

Useful iterations: 2 (238.0ms)

Iter	Nodes	Cost
0	149	1251
1	327	1018
2	905	918
3	2962	918
done	5000	918

prune331.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.7b	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) t x)
3.5b	(cbrt (/ (- y z) (- a z)))
3.5b	(cbrt (/ (- y z) (- a z)))
3.5b	(cbrt (/ (- y z) (- a z)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

97×	`add-sqr-sqrt` `*-un-lft-identity`
93×	`cbrt-prod`
75×	`times-frac`
37×	`add-cube-cbrt`
30×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-div` `flip3--` `pow1/3` `flip--` `div-inv`
1×	`fma-udef`

Counts

4 → 136

Calls

4 calls:

1.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) t x)
20.0ms	(cbrt (/ (- y z) (- a z)))
20.0ms	(cbrt (/ (- y z) (- a z)))
21.0ms	(cbrt (/ (- y z) (- a z)))

series1.8s

Counts

4 → 12

Calls

4 calls:

136.0ms	(fma (* (* (cbrt (/ (- y z) (- a z))) (cbrt (/ (- y z) (- a z)))) (cbrt (/ (- y z) (- a z)))) t x)
577.0ms	(cbrt (/ (- y z) (- a z)))
565.0ms	(cbrt (/ (- y z) (- a z)))
528.0ms	(cbrt (/ (- y z) (- a z)))

simplify3.8s

Counts

148 → 148

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	175	2777
1	332	2684
2	667	2387
3	1548	2327
4	4217	2261
done	5000	2258

prune844.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (fma (/ (- y z) (- a z)) t x))
1.7b	(fma (/ (- y z) (- a z)) t x)
1.7b	(fma (/ (- y z) (- a z)) t x)
1.7b	(fma (/ (- y z) (- a z)) t x)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `fma-udef`
1×	`pow1/3`

Counts

4 → 43

Calls

4 calls:

2.0ms	(cbrt (fma (/ (- y z) (- a z)) t x))
1.0ms	(fma (/ (- y z) (- a z)) t x)
1.0ms	(fma (/ (- y z) (- a z)) t x)
1.0ms	(fma (/ (- y z) (- a z)) t x)

series1.4s

Counts

4 → 12

Calls

4 calls:

907.0ms	(cbrt (fma (/ (- y z) (- a z)) t x))
165.0ms	(fma (/ (- y z) (- a z)) t x)
170.0ms	(fma (/ (- y z) (- a z)) t x)
139.0ms	(fma (/ (- y z) (- a z)) t x)

simplify2.7s

Counts

55 → 55

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	60	737
1	119	732
2	276	647
3	880	641
4	3335	633
done	5000	629

prune311.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0.0b

regimes384.0ms

Accuracy

58.2% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 1.4b

bsearch105.0ms

Steps

Iters	Range		Point
6	1.230628501312938e-151	7.040558363340882e-151	2.6621744974944237e-151
7	-1.16580668397101e-45	-2.865294902316071e-47	-7.122674290888581e-47

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	39
1	23	30
done	23	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

671.0ms	8724×	body	80	valid
0.0ms	2×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	2560	valid