Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	241×	body	80	valid
5.0ms	18×	body	640	valid
5.0ms	25×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	8×	body	160	valid

simplify6.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
6	2502
5	895
4	343
3	126
2	46
1	23
0	11

prune45.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.0b

localize70.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
16.1b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite92.0ms

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:

84.0ms	(/ (- t x) (- a z))
3.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series300.0ms

Counts

2 → 6

Calls

2 calls:

103.0ms	(/ (- t x) (- a z))
197.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify4.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	2139
2	660
1	276
0	120

prune1.3s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.6b

localize110.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
16.1b	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

rewrite218.0ms

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:

28.0ms	(/ 1 (- a z))
172.0ms	(* (- t x) (/ 1 (- a z)))
1.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series395.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ 1 (- a z))
117.0ms	(* (- t x) (/ 1 (- a z)))
205.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify7.5s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
3	4043
2	1308
1	373
0	158

prune1.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.4b

localize101.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.3b	(+ (/ (- y z) (/ (- a z) (- t x))) x)
4.8b	(/ (- y z) (/ (- a z) (- t x)))

rewrite723.0ms

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` `insert-posit16` `log1p-expm1-u`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log` `flip3-+` `associate-+l-` `flip-+` `distribute-lft-out`

Counts

3 → 443

Calls

3 calls:

86.0ms	(/ (- a z) (- t x))
465.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
99.0ms	(/ (- y z) (/ (- a z) (- t x)))

series1.2s

Counts

3 → 9

Calls

3 calls:

113.0ms	(/ (- a z) (- t x))
424.0ms	(+ (/ (- y z) (/ (- a z) (- t x))) x)
666.0ms	(/ (- y z) (/ (- a z) (- t x)))

simplify6.7s

Counts

452 → 452

Iterations

Iter	Nodes
done	5001
2	3834
1	1152
0	361

prune5.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.7b

localize125.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- t x))
3.4b	(/ y (/ (- a z) (- t x)))
4.1b	(- (/ z (/ (- a z) (- t x))) x)
4.2b	(/ z (/ (- a z) (- t x)))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

1086×	`times-frac`
959×	`add-sqr-sqrt`
952×	`*-un-lft-identity`
526×	`add-cube-cbrt`
294×	`prod-diff`
215×	`difference-of-squares`
213×	`distribute-lft-out--`
98×	`fma-neg`
67×	`associate-/r*`
48×	`associate-/r/`
27×	`div-inv`
23×	`flip3--` `flip--`
16×	`add-cbrt-cube` `add-exp-log`
11×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 756

Calls

4 calls:

107.0ms	(/ (- a z) (- t x))
80.0ms	(/ y (/ (- a z) (- t x)))
513.0ms	(- (/ z (/ (- a z) (- t x))) x)
99.0ms	(/ z (/ (- a z) (- t x)))

series970.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- a z) (- t x))
274.0ms	(/ y (/ (- a z) (- t x)))
242.0ms	(- (/ z (/ (- a z) (- t x))) x)
369.0ms	(/ z (/ (- a z) (- t x)))

simplify3.7s

Counts

768 → 768

Iterations

Iter	Nodes
done	5000
1	1749
0	680

prune8.3s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 5.5b

regimes3.1s

Accuracy

17.4% (5.7b remaining)

Error of 9.7b against oracle of 4.0b and baseline of 10.9b

bsearch229.0ms

Steps

Iters	Range		Point
7	2.016995608420584e-153	1.0792454867241964e-151	1.5453516653821514e-152
10	-3.7853197546515783e-110	-1.648318488097239e-120	-1.7262808088606156e-120

simplify24.0ms

Iterations

Iter	Nodes
done	27
1	27
0	23

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	7731×	body	80	valid
229.0ms	474×	body	640	valid
188.0ms	290×	body	1280	valid
113.0ms	419×	body	320	valid
82.0ms	296×	body	160	valid
9.0ms	18×	body	2560	valid