Details

sample78.0ms

Algorithm

intervals

Results

29.0ms	249×	body	80	valid
6.0ms	19×	body	640	valid
4.0ms	10×	body	1280	valid
3.0ms	15×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify9.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (32.0ms)

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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:

26.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series304.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/ (- y z) (- a z))
221.0ms	(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

prune323.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.4b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.8b	(* (/ (- y z) (- a z)) (- t x))
2.8b	(+ (* (/ (- y z) (- a z)) (- t x)) x)

rewrite168.0ms

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:

32.0ms	(/ (- y z) (- a z))
87.0ms	(* (/ (- y z) (- a z)) (- t x))
33.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

series963.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(/ (- y z) (- a z))
550.0ms	(* (/ (- y z) (- a z)) (- t x))
305.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)

simplify1.6s

Counts

179 → 179

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	255	3085
1	665	2718
2	1955	2494
done	5001	2468

prune784.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.4b

localize15.0ms

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)

rewrite92.0ms

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:

45.0ms	(/ (- a z) (- y z))
30.0ms	(/ 1 (/ (- a z) (- y z)))
1.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

series534.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (- a z) (- y z))
230.0ms	(/ 1 (/ (- a z) (- y z)))
209.0ms	(fma (/ 1 (/ (- a z) (- y z))) (- t x) x)

simplify2.9s

Counts

223 → 223

Iterations

Useful iterations: done (2.9s)

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

prune609.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.8b	(/ (- t x) (/ (- a z) (- y z)))
2.8b	(+ (/ (- t x) (/ (- a z) (- y z))) x)

rewrite393.0ms

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:

54.0ms	(/ (- a z) (- y z))
80.0ms	(/ (- t x) (/ (- a z) (- y z)))
220.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

series617.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(/ (- a z) (- y z))
271.0ms	(/ (- t x) (/ (- a z) (- y z)))
260.0ms	(+ (/ (- t x) (/ (- a z) (- y z))) x)

simplify1.7s

Counts

449 → 449

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	360	6052
1	1023	5695
2	3693	5544
done	5000	5542

prune2.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.3b

regimes353.0ms

Accuracy

27.1% (6.1b remaining)

Error of 9.6b against oracle of 3.5b and baseline of 11.9b

bsearch170.0ms

Steps

Iters	Range		Point
10	2.7753413219507016e+156	1.5853395761105443e+166	4.892583137041057e+158
9	-1.7910089691738227e+194	-1.8921491898552533e+186	-1.0577972736928619e+192

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	20	39
1	25	31
done	25	31

end0.0ms

sample1.7s

Algorithm

intervals

Results

688.0ms	7808×	body	80	valid
134.0ms	482×	body	640	valid
105.0ms	414×	body	320	valid
76.0ms	270×	body	1280	valid
63.0ms	283×	body	160	valid
9.0ms	25×	body	2560	valid