Details

sample39.0ms

Algorithm

intervals

Results

15.0ms	252×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 3 (15.0ms)

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

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
15.4b	(fma (/ (- y x) (- a t)) (- z t) 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-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:

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

series184.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(/ (- y x) (- a t))
120.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify2.3s

Counts

70 → 70

Iterations

Useful iterations: 3 (849.0ms)

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

prune259.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
2.8b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
6.4b	(* (/ (- y x) (- a t)) (- z t))

rewrite162.0ms

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:

32.0ms	(/ (- y x) (- a t))
33.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
86.0ms	(* (/ (- y x) (- a t)) (- z t))

series584.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- y x) (- a t))
192.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
293.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify1.9s

Counts

179 → 179

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	256	3107
1	719	2752
2	3321	2516
done	5001	2490

prune628.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.0b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite166.0ms

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	(/ (- z t) (- a t))
83.0ms	(* (- y x) (/ (- z t) (- a t)))
46.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

series395.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(/ (- z t) (- a t))
132.0ms	(* (- y x) (/ (- z t) (- a t)))
204.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)

simplify1.8s

Counts

135 → 135

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	189	1881
1	519	1777
2	2652	1675
done	5002	1667

prune485.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.5b

localize20.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- z t) (- a t))
3.1b	(fma (- y x) (/ (- z t) (- a t)) x)

rewrite46.0ms

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:

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

series266.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (- z t) (- a t))
185.0ms	(fma (- y x) (/ (- z t) (- a t)) x)

simplify2.8s

Counts

70 → 70

Iterations

Useful iterations: 3 (815.0ms)

Iter	Nodes	Cost
0	116	918
1	272	890
2	855	840
3	4653	836
done	5000	836

prune242.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

regimes492.0ms

Accuracy

17.2% (6.8b remaining)

Error of 10.4b against oracle of 3.6b and baseline of 11.9b

bsearch102.0ms

Steps

Iters	Range		Point
6	1.2730776164824128e-169	1.9699776342459955e-168	2.3214927699090608e-169
4	-5.362570321076992e-137	-3.5594867624673915e-137	-3.8376314895751423e-137

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	48
1	30	35
done	30	35

end0.0ms

sample1.6s

Algorithm

intervals

Results

613.0ms	7716×	body	80	valid
179.0ms	426×	body	320	valid
105.0ms	498×	body	640	valid
68.0ms	295×	body	160	valid
66.0ms	245×	body	1280	valid
5.0ms	13×	body	2560	valid