Details

sample70.0ms

Algorithm

intervals

Results

31.0ms	258×	body	80	valid
4.0ms	17×	body	320	valid
2.0ms	6×	body	1280	valid
2.0ms	7×	body	640	valid
1.0ms	7×	body	160	valid

simplify6.6s

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.4b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
13.5b	(fma (/ (- t x) (- a z)) (- y z) x)

rewrite38.0ms

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:

30.0ms	(/ (- t x) (- a z))
1.0ms	(fma (/ (- t x) (- a z)) (- y z) x)

series193.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(/ (- t x) (- a z))
130.0ms	(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

prune265.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a z) (- t x))
0.5b	(/ 1 (/ (- a z) (- t x)))
13.5b	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

rewrite96.0ms

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:

30.0ms	(/ (- a z) (- t x))
51.0ms	(/ 1 (/ (- a z) (- t x)))
1.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

series473.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (- a z) (- t x))
244.0ms	(/ 1 (/ (- a z) (- t x)))
169.0ms	(fma (/ 1 (/ (- a z) (- t x))) (- y z) x)

simplify2.6s

Counts

223 → 223

Iterations

Useful iterations: done (2.6s)

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

prune573.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.8b	(+ (* (/ (- t x) (- a z)) (- y z)) x)
7.4b	(* (/ (- t x) (- a z)) (- y z))

rewrite196.0ms

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:

43.0ms	(/ (- t x) (- a z))
39.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
98.0ms	(* (/ (- t x) (- a z)) (- y z))

series560.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(/ (- t x) (- a z))
208.0ms	(+ (* (/ (- t x) (- a z)) (- y z)) x)
294.0ms	(* (/ (- t x) (- a z)) (- y z))

simplify1.3s

Counts

179 → 179

Iterations

Useful iterations: done (1.3s)

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

prune579.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.2b	(* (- t x) (/ (- y z) (- a z)))
2.3b	(+ (* (- t x) (/ (- y z) (- a z))) x)

rewrite124.0ms

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:

27.0ms	(/ (- y z) (- a z))
61.0ms	(* (- t x) (/ (- y z) (- a z)))
31.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

series358.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- y z) (- a z))
127.0ms	(* (- t x) (/ (- y z) (- a z)))
176.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)

simplify1.6s

Counts

135 → 135

Iterations

Useful iterations: done (1.6s)

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

prune502.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 2.6b

regimes349.0ms

Accuracy

0.8% (7.8b remaining)

Error of 11.5b against oracle of 3.7b and baseline of 11.5b

bsearch74.0ms

Steps

Iters	Range		Point
9	-1.816126690174146e+173	-5.346400383434256e+167	-2.065198081982861e+170

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	29
1	22	29
done	22	29

end0.0ms

sample1.7s

Algorithm

intervals

Results

733.0ms	7750×	body	80	valid
115.0ms	442×	body	320	valid
95.0ms	445×	body	640	valid
72.0ms	267×	body	1280	valid
30.0ms	255×	body	160	valid
5.0ms	14×	body	2560	valid