Details

sample43.0ms

Algorithm

intervals

Results

18.0ms	255×	body	80	valid
3.0ms	20×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	6×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1910
5	805
4	299
3	108
2	43
1	20
0	11

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
14.7b	(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:

26.0ms	(/ (- t x) (- a z))
0.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series181.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(/ (- t x) (- a z))
110.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.5s

Counts

70 → 70

Iterations

Iter	Nodes
done	5045
3	2171
2	671
1	274
0	118

prune393.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.2b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.4b	(/ 1 (/ (- a z) (- t x)))
14.7b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite72.0ms

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

Counts

3 → 214

Calls

3 calls:

25.0ms	(/ (- a z) (- t x))
37.0ms	(/ 1 (/ (- a z) (- t x)))
0.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series502.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (- a z) (- t x))
259.0ms	(/ 1 (/ (- a z) (- t x)))
176.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify1.7s

Counts

223 → 223

Iterations

Iter	Nodes
done	5000
2	2270
1	708
0	274

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.5b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
5.0b	(* (/ (- t x) (- a z)) (- y z))

rewrite150.0ms

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:

28.0ms	(/ (- t x) (- a z))
32.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
79.0ms	(* (/ (- t x) (- a z)) (- y z))

series593.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(/ (- t x) (- a z))
223.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
291.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.8s

Counts

179 → 179

Iterations

Iter	Nodes
done	5000
2	1995
1	712
0	256

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.7b	(+ (* (- t x) (/ (- y z) (- a z))) x)
3.5b	(* (- t x) (/ (- y z) (- a z)))

rewrite142.0ms

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))
28.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
78.0ms	(* (- t x) (/ (- y z) (- a z)))

series365.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- y z) (- a z))
174.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
138.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify1.3s

Counts

135 → 135

Iterations

Iter	Nodes
done	5000
2	1759
1	517
0	189

prune632.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.6b

regimes842.0ms

Accuracy

29.3% (5.7b remaining)

Error of 9.3b against oracle of 3.6b and baseline of 11.7b

bsearch151.0ms

Steps

Iters	Range		Point
11	5.1631975674819804e-138	5.42072859804174e-111	6.7132731075641235e-136
8	-1.6522177722814347e-125	-5.998325240897579e-128	-3.0582848762601583e-127

simplify5.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample1.4s

Algorithm

intervals

Results

696.0ms	7883×	body	80	valid
130.0ms	484×	body	640	valid
89.0ms	425×	body	320	valid
68.0ms	270×	body	1280	valid
25.0ms	229×	body	160	valid
4.0ms	13×	body	2560	valid