Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	242×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	8×	body	1280	valid
1.0ms	9×	body	160	valid

simplify7.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	11	13
1	23	13
2	46	12
3	128	12
4	360	12
5	877	12
6	2016	12
7	3586	12
done	5000	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.1b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite49.0ms

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:

46.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series196.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(/ (- t x) (- a z))
137.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.3s

Counts

70 → 70

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	118	918
1	269	890
2	658	838
3	1743	834
done	5000	830

prune372.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
15.0b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite116.0ms

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:

43.0ms	(/ (- a z) (- t x))
56.0ms	(/ 1 (/ (- a z) (- t x)))
1.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series648.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- a z) (- t x))
339.0ms	(/ 1 (/ (- a z) (- t x)))
209.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify3.0s

Counts

223 → 223

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	274	3778
1	617	3266
2	1425	2943
3	4015	2863
done	5001	2861

prune700.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 8.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (/ 1 (- a z)) (- t x))
15.0b	(fma (* (/ 1 (- a z)) (- t x)) (- y z) x)

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
35×	`add-cube-cbrt`
32×	`times-frac`
21×	`associate-l`
18×	`prod-diff`
16×	`add-exp-log`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-r` `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` `sub-neg` `rec-exp` `1-exp` `associate-*r/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 126

Calls

3 calls:

19.0ms	(/ 1 (- a z))
73.0ms	(* (/ 1 (- a z)) (- t x))
0.0ms	(fma (* (/ 1 (- a z)) (- t x)) (- y z) x)

series527.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(/ 1 (- a z))
276.0ms	(* (/ 1 (- a z)) (- t x))
203.0ms	(fma (* (/ 1 (- a z)) (- t x)) (- y z) x)

simplify2.4s

Counts

135 → 135

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	213	1961
1	488	1582
2	1217	1312
3	3914	1266
done	5000	1264

prune400.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 8.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.9b	(+ x (* (- y z) (/ (- t x) (- a z))))
4.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 128

Calls

3 calls:

50.0ms	(/ (- t x) (- a z))
15.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
106.0ms	(* (- y z) (/ (- t x) (- a z)))

series501.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (- t x) (- a z))
246.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
188.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify1.2s

Counts

137 → 137

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	189	1881
1	484	1769
2	1787	1659
done	5002	1657

prune351.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.6b

regimes393.0ms

Accuracy

23.4% (8.7b remaining)

Error of 12.5b against oracle of 3.8b and baseline of 15.2b

bsearch144.0ms

Steps

Iters	Range		Point
8	1.3793369693960326e-72	4.61238746493178e-68	7.030593888359201e-71
9	-4.494716191071896e-101	-1.1624215725433809e-108	-2.3466275089520125e-107

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	51
1	35	51
done	35	51

end0.0ms

sample1.8s

Algorithm

intervals

Results

937.0ms	7745×	body	80	valid
200.0ms	482×	body	640	valid
122.0ms	441×	body	320	valid
82.0ms	261×	body	1280	valid
35.0ms	278×	body	160	valid
4.0ms	12×	body	2560	valid