Details

sample69.0ms

Algorithm

intervals

Results

29.0ms	234×	body	80	valid
4.0ms	13×	body	640	valid
4.0ms	16×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	11×	body	160	valid
1.0ms	1×	body	2560	valid

simplify6.7s

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.9b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite37.0ms

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:

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

series218.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(/ (- t x) (- a z))
120.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

simplify1.7s

Counts

70 → 70

Iterations

Useful iterations: done (1.7s)

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

prune291.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.8b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.8b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
6.3b	(* (/ (- t x) (- a z)) (- y z))

rewrite158.0ms

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:

29.0ms	(/ (- t x) (- a z))
34.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
75.0ms	(* (/ (- t x) (- a z)) (- y z))

series583.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(/ (- t x) (- a z))
223.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
283.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.7s

Counts

179 → 179

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	256	3107
1	665	2740
2	1928	2516
done	5002	2490

prune688.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.0b	(* (- t x) (/ (- y z) (- a z)))
2.5b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite154.0ms

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-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` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

32.0ms	(/ (- y z) (- a z))
82.0ms	(* (- t x) (/ (- y z) (- a z)))
31.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series497.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(/ (- y z) (- a z))
176.0ms	(* (- t x) (/ (- y z) (- a z)))
253.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify1.4s

Counts

135 → 135

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	189	1881
1	486	1765
2	1770	1669
done	5001	1667

prune613.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- a z) (- y z))
0.2b	(/ 1 (/ (- a z) (- y z)))
2.0b	(* (- t x) (/ 1 (/ (- a z) (- y z))))
2.5b	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

rewrite244.0ms

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×	`add-exp-log` `associate-/r*`
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` `log1p-expm1-u`
3×	`cbrt-unprod`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `fma-def` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 353

Calls

4 calls:

43.0ms	(/ (- a z) (- y z))
26.0ms	(/ 1 (/ (- a z) (- y z)))
117.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))
33.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

series813.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (- a z) (- y z))
227.0ms	(/ 1 (/ (- a z) (- y z)))
291.0ms	(* (- t x) (/ 1 (/ (- a z) (- y z))))
232.0ms	(+ (* (- t x) (/ 1 (/ (- a z) (- y z)))) x)

simplify2.4s

Counts

365 → 365

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	403	6260
1	998	5130
2	2757	4711
done	5000	4633

prune890.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.4b

regimes431.0ms

Accuracy

16.1% (6.9b remaining)

Error of 10.3b against oracle of 3.4b and baseline of 11.6b

bsearch249.0ms

Steps

Iters	Range		Point
5	7.705379630644969e-17	2.017679358261303e-16	7.829350447579145e-17
10	4.4245337053054734e-42	7.844867681217723e-32	7.107129072265313e-32
7	9.980803508188452e-191	4.2019731998712036e-189	7.280294648575056e-190
7	-1.9408587555071196e-141	-1.9883461805222869e-143	-3.13107925058598e-143

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	34	85
1	42	79
done	42	79

end0.0ms

sample1.5s

Algorithm

intervals

Results

591.0ms	7725×	body	80	valid
168.0ms	480×	body	640	valid
91.0ms	272×	body	1280	valid
68.0ms	418×	body	320	valid
28.0ms	265×	body	160	valid
3.0ms	10×	body	2560	valid