Details

sample75.0ms

Algorithm

intervals

Results

29.0ms	242×	body	80	valid
8.0ms	18×	body	640	valid
7.0ms	12×	body	1280	valid
5.0ms	15×	body	320	valid
2.0ms	7×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.2b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite22.0ms

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/` `insert-posit16` `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 → 66

Calls

2 calls:

21.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series230.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(/ (- t x) (- a z))
146.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify2.3s

Counts

72 → 72

Iterations

Iter	Nodes
done	5002
3	2212
2	671
1	276
0	120

prune488.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.3b

localize28.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.7b	(* (/ (- t x) (- a z)) (- y z))
4.2b	(+ (* (/ (- t x) (- a z)) (- y z)) x)

rewrite119.0ms

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` `insert-posit16` `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 → 173

Calls

3 calls:

35.0ms	(/ (- t x) (- a z))
50.0ms	(* (/ (- t x) (- a z)) (- y z))
28.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)

series645.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(/ (- t x) (- a z))
304.0ms	(* (/ (- t x) (- a z)) (- y z))
260.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)

simplify1.8s

Counts

182 → 182

Iterations

Iter	Nodes
done	5005
2	1982
1	716
0	259

prune1.0s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.2b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.1b	(* (- t x) (/ (- y z) (- a z)))
3.0b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite123.0ms

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` `insert-posit16` `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 → 129

Calls

3 calls:

29.0ms	(/ (- y z) (- a z))
52.0ms	(* (- t x) (/ (- y z) (- a z)))
39.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series474.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ (- y z) (- a z))
164.0ms	(* (- t x) (/ (- y z) (- a z)))
245.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify1.7s

Counts

138 → 138

Iterations

Iter	Nodes
done	5001
2	1770
1	521
0	192

prune750.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.3b	(/ 1 (/ (- a z) (- y z)))
2.1b	(* (- t x) (/ 1 (/ (- a z) (- y z))))
3.0b	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
338×	`add-sqr-sqrt`
326×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
83×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*` `add-exp-log`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
11×	`flip3--` `flip--`
10×	`div-inv`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`associate-l` `unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`+-commutative` `sum-log` `fma-def` `flip3-+` `div-sub` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `flip-+` `pow-flip` `inv-pow`

Counts

4 → 357

Calls

4 calls:

28.0ms	(/ (- a z) (- y z))
16.0ms	(/ 1 (/ (- a z) (- y z)))
60.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))
39.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

series803.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(/ (- a z) (- y z))
186.0ms	(/ 1 (/ (- a z) (- y z)))
286.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))
232.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

simplify2.4s

Counts

369 → 369

Iterations

Iter	Nodes
done	5000
2	3828
1	1179
0	407

prune1.8s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.5b

regimes842.0ms

Accuracy

30.9% (5.8b remaining)

Error of 9.3b against oracle of 3.5b and baseline of 11.9b

bsearch247.0ms

Steps

Iters	Range		Point
8	8.883612526165312e-94	2.7867056099957307e-91	9.426461174744231e-94
9	-1.4460141652926686e-143	-1.322453988461606e-151	-1.2559578325599803e-148

simplify6.0ms

Iterations

Iter	Nodes
done	33
1	33
0	24

end0.0ms

sample2.4s

Algorithm

intervals

Results

995.0ms	7793×	body	80	valid
589.0ms	474×	body	640	valid
194.0ms	288×	body	1280	valid
163.0ms	435×	body	320	valid
51.0ms	258×	body	160	valid
11.0ms	20×	body	2560	valid