Details

sample32.0ms

Algorithm

intervals

Results

10.0ms	258×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	9×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	11	245
1	23	245
2	46	220
3	128	220
4	367	220
5	1129	220
6	4619	220
done	5000	220

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
11.8b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite28.0ms

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/` `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 → 64

Calls

2 calls:

24.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series219.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(/ (- t x) (- a z))
150.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.4s

Counts

70 → 70

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	118	18729
1	274	17805
2	848	17725
3	4626	17645
done	5000	17645

prune521.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
11.8b	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

rewrite77.0ms

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` `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 → 105

Calls

3 calls:

18.0ms	(/ 1 (- a z))
53.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

series264.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ 1 (- a z))
89.0ms	(* (- t x) (/ 1 (- a z)))
124.0ms	(fma (* (- t x) (/ 1 (- a z))) (- y z) x)

simplify4.6s

Counts

114 → 114

Iterations

Useful iterations: done (4.6s)

Iter	Nodes	Cost
0	155	26946
1	373	21436
2	2967	19673
done	5001	19502

prune710.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 6.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
0.9b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
6.3b	(* (/ (- t x) (- a z)) (- y z))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 170

Calls

3 calls:

41.0ms	(/ (- t x) (- a z))
42.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
81.0ms	(* (/ (- t x) (- a z)) (- y z))

series597.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(/ (- t x) (- a z))
226.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
303.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify2.2s

Counts

179 → 179

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	256	61728
1	717	56140
2	3330	50842
done	5001	50712

prune1.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.7b	(+ (* (- t x) (/ (- y z) (- a z))) x)
2.9b	(* (- t x) (/ (- y z) (- a z)))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

29.0ms	(/ (- y z) (- a z))
19.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
66.0ms	(* (- t x) (/ (- y z) (- a z)))

series520.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(/ (- y z) (- a z))
272.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
177.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify2.5s

Counts

135 → 135

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	189	37921
1	517	34642
2	2647	34051
done	5001	34001

prune786.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.3b

regimes696.0ms

Accuracy

6.4% (7.5b remaining)

Error of 11.2b against oracle of 3.7b and baseline of 11.7b

bsearch65.0ms

Steps

Iters	Range		Point
9	6.232674112580621e+208	4.457444719923058e+213	1.5167274174856026e+213

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	632
1	27	632
done	27	632

end0.0ms

sample1.8s

Algorithm

intervals

Results

566.0ms	7795×	body	80	valid
467.0ms	393×	body	320	valid
150.0ms	287×	body	1280	valid
105.0ms	488×	body	640	valid
43.0ms	16×	body	2560	valid
28.0ms	249×	body	160	valid