Details

sample62.0ms

Algorithm

intervals

Results

19.0ms	242×	body	80	valid
4.0ms	14×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	4×	body	1280	valid
0.0ms	1×	body	2560	valid

simplify9.6s

Counts

1 → 1

Iterations

Useful iterations: 3 (33.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	322	12
5	766	12
6	1555	12
7	2873	12
8	4761	12
done	5000	12

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite43.0ms

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:

40.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series261.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ (- y z) (- a z))
182.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify1.8s

Counts

70 → 70

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	116	918
1	266	890
2	653	838
3	1707	834
done	5001	830

prune299.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.0b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.3b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.4b	(* (/ (- y z) (- a z)) (- t x))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

42.0ms	(/ (- y z) (- a z))
64.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
123.0ms	(* (/ (- y z) (- a z)) (- t x))

series809.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ (- y z) (- a z))
295.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
450.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify1.6s

Counts

179 → 179

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	255	3085
1	665	2718
2	1939	2494
done	5002	2468

prune776.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.3b	(/ 1 (/ (- a z) (- y z)))
3.3b	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

rewrite128.0ms

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--` `flip--` `div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `div-sub` `fma-udef` `inv-pow`

Counts

3 → 214

Calls

3 calls:

53.0ms	(/ (- a z) (- y z))
52.0ms	(/ 1 (/ (- a z) (- y z)))
1.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

series448.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(/ (- a z) (- y z))
210.0ms	(/ 1 (/ (- a z) (- y z)))
177.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify3.3s

Counts

223 → 223

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	273	3782
1	615	3270
2	1414	2947
3	3930	2867
done	5002	2865

prune617.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.9b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
2.3b	(+ (/ (- t x) (/ (- a z) (- y z))) x)
2.5b	(/ (- t x) (/ (- a z) (- y z)))

rewrite488.0ms

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--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

42.0ms	(/ (- a z) (- y z))
286.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
90.0ms	(/ (- t x) (/ (- a z) (- y z)))

series708.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ (- a z) (- y z))
254.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)
376.0ms	(/ (- t x) (/ (- a z) (- y z)))

simplify1.9s

Counts

449 → 449

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	360	6052
1	1023	5695
2	3699	5544
done	5001	5542

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.9b

regimes620.0ms

Accuracy

21.8% (6.8b remaining)

Error of 10.0b against oracle of 3.2b and baseline of 11.9b

bsearch196.0ms

Steps

Iters	Range		Point
11	1.270532878618462e-164	2.6487703454575654e-144	7.692781660197599e-150
8	-4.128450568952297e-153	-5.6397930640659014e-157	-4.046536476058794e-154

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	24	50
1	32	36
done	32	36

end0.0ms

sample1.7s

Algorithm

intervals

Results

635.0ms	7761×	body	80	valid
169.0ms	474×	body	640	valid
115.0ms	281×	body	1280	valid
110.0ms	431×	body	320	valid
30.0ms	275×	body	160	valid
5.0ms	15×	body	2560	valid