Details

sample44.0ms

Algorithm

intervals

Results

17.0ms	255×	body	80	valid
3.0ms	16×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	6×	body	1280	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	2560	valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (17.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	326	12
5	1002	12
6	3984	12
done	5000	12

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
14.3b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite58.0ms

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:

52.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series254.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(/ (- y x) (- a t))
153.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify2.7s

Counts

70 → 70

Iterations

Useful iterations: 3 (822.0ms)

Iter	Nodes	Cost
0	118	918
1	275	890
2	851	838
3	4610	836
done	5000	836

prune487.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.6b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- y x) (/ 1 (- a t)))
14.2b	(fma (* (- y x) (/ 1 (- a t))) (- z t) 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-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

14.0ms	(/ 1 (- a t))
58.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series378.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ 1 (- a t))
122.0ms	(* (- y x) (/ 1 (- a t)))
180.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify6.4s

Counts

114 → 114

Iterations

Useful iterations: done (6.4s)

Iter	Nodes	Cost
0	155	1285
1	374	1129
2	2964	954
done	5001	952

prune644.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.6b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
0.5b	(/ 1 (/ (- a t) (- y x)))
14.3b	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

rewrite102.0ms

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:

42.0ms	(/ (- a t) (- y x))
42.0ms	(/ 1 (/ (- a t) (- y x)))
1.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

series601.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (- a t) (- y x))
319.0ms	(/ 1 (/ (- a t) (- y x)))
188.0ms	(fma (/ 1 (/ (- a t) (- y x))) (- z t) x)

simplify1.6s

Counts

223 → 223

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	274	3778
1	716	3266
2	3379	3035
done	5001	3029

prune808.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 7.6b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- y x))
4.0b	(+ (/ (- z t) (/ (- a t) (- y x))) x)
5.2b	(/ (- z t) (/ (- a t) (- y x)))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

610×	`times-frac`
572×	`*-un-lft-identity`
570×	`add-sqr-sqrt`
200×	`add-cube-cbrt`
185×	`distribute-lft-out--` `difference-of-squares`
160×	`fma-def`
36×	`associate-/r*`
26×	`associate-/r/`
14×	`flip3--` `flip--` `div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `log1p-expm1-u`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+l-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 440

Calls

3 calls:

44.0ms	(/ (- a t) (- y x))
241.0ms	(+ (/ (- z t) (/ (- a t) (- y x))) x)
54.0ms	(/ (- z t) (/ (- a t) (- y x)))

series853.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (- a t) (- y x))
288.0ms	(+ (/ (- z t) (/ (- a t) (- y x))) x)
472.0ms	(/ (- z t) (/ (- a t) (- y x)))

simplify791.0ms

Counts

449 → 449

Iterations

Useful iterations: done (768.0ms)

Iter	Nodes	Cost
0	358	6030
1	1158	5727
done	5001	5528

prune2.3s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 5.3b

regimes940.0ms

Accuracy

-2.4% (8.5b remaining)

Error of 11.8b against oracle of 3.3b and baseline of 11.6b

bsearch135.0ms

Steps

Iters	Range		Point
4	-6.052045417163306e-253	-4.224751207741741e-253	-4.3681140934149486e-253
10	-1.4677513957497507e-191	-2.8514417684493804e-201	-8.932233526672919e-192

simplify10.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	29	56
1	35	54
2	36	54
done	36	54

end0.0ms

sample1.6s

Algorithm

intervals

Results

607.0ms	7789×	body	80	valid
186.0ms	483×	body	640	valid
98.0ms	410×	body	320	valid
95.0ms	265×	body	1280	valid
26.0ms	253×	body	160	valid
5.0ms	16×	body	2560	valid