Details

sample44.0ms

Algorithm

intervals

Results

13.0ms	246×	body	80	valid
3.0ms	17×	body	640	valid
2.0ms	15×	body	320	valid
2.0ms	7×	body	1280	valid
1.0ms	14×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 3 (14.0ms)

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize15.0ms

Local error

Found 1 expressions with local error:

15.0b

(fma (/ (- y x) (- a t)) (- z t) x)

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (/ (- y x) (- a t)) (- z t) x)

series131.0ms

Counts

1 → 3

Calls

1 calls:

131.0ms

(fma (/ (- y x) (- a t)) (- z t) x)

simplify980.0ms

Counts

13 → 13

Iterations

Useful iterations: done (979.0ms)

Iter	Nodes	Cost
0	26	194
1	50	194
2	108	170
3	337	168
4	1735	162
done	5001	160

prune61.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.5b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.5b	(* (/ (- z t) (- a t)) (- y x))
3.8b	(+ (* (/ (- z t) (- a t)) (- y x)) x)

rewrite130.0ms

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:

23.0ms	(/ (- z t) (- a t))
66.0ms	(* (/ (- z t) (- a t)) (- y x))
27.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

series635.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(/ (- z t) (- a t))
362.0ms	(* (/ (- z t) (- a t)) (- y x))
212.0ms	(+ (* (/ (- z t) (- a t)) (- y x)) x)

simplify1.5s

Counts

179 → 179

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	255	3085
1	717	2731
2	3221	2494
done	5000	2468

prune610.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- z t) (- a t))
0.0b	(/ (- z t) (- a t))
0.8b	(* (/ (- z t) (- a t)) y)
5.5b	(fma (/ (- z t) (- a t)) (- x) x)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
108×	`*-un-lft-identity`
76×	`times-frac`
40×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-l`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r` `associate-/l`
6×	`pow1` `associate-/r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`frac-2neg` `div-sub` `prod-exp` `clear-num` `cbrt-unprod` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 170

Calls

4 calls:

34.0ms	(/ (- z t) (- a t))
32.0ms	(/ (- z t) (- a t))
45.0ms	(* (/ (- z t) (- a t)) y)
0.0ms	(fma (/ (- z t) (- a t)) (- x) x)

series413.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (- z t) (- a t))
66.0ms	(/ (- z t) (- a t))
137.0ms	(* (/ (- z t) (- a t)) y)
139.0ms	(fma (/ (- z t) (- a t)) (- x) x)

simplify1.1s

Counts

182 → 182

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	162	2228
1	406	2164
2	1563	2038
done	5000	2030

prune699.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 3.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- z t) (- a t))
0.7b	(/ 1 (/ (- a t) (- z t)))
0.8b	(* (/ (- z t) (- a t)) y)
5.5b	(fma (/ 1 (/ (- a t) (- z t))) (- x) x)

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

244×	`times-frac`
233×	`add-sqr-sqrt`
228×	`*-un-lft-identity`
104×	`add-cube-cbrt`
62×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
31×	`associate-l`
22×	`add-exp-log`
16×	`add-cbrt-cube`
13×	`associate-/r/`
9×	`div-exp`
8×	`associate-/l*`
7×	`pow1` `flip3--` `flip--` `div-inv`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`rec-exp` `frac-2neg` `1-exp` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`pow-flip` `div-sub` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 266

Calls

4 calls:

26.0ms	(/ (- z t) (- a t))
30.0ms	(/ 1 (/ (- a t) (- z t)))
43.0ms	(* (/ (- z t) (- a t)) y)
0.0ms	(fma (/ 1 (/ (- a t) (- z t))) (- x) x)

series531.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (- z t) (- a t))
177.0ms	(/ 1 (/ (- a t) (- z t)))
127.0ms	(* (/ (- z t) (- a t)) y)
157.0ms	(fma (/ 1 (/ (- a t) (- z t))) (- x) x)

simplify2.1s

Counts

278 → 278

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	355	4372
1	920	3852
2	4900	3631
done	5000	3621

prune790.0ms

Pruning

20 alts after pruning (18 fresh and 2 done)

Merged error: 3.5b

regimes540.0ms

Accuracy

7.8% (4.3b remaining)

Error of 7.9b against oracle of 3.6b and baseline of 8.2b

bsearch120.0ms

Steps

Iters	Range		Point
9	2.0512714046454485e-79	8.745691868853264e-72	2.0847579098207242e-79
9	-3.611707952239078e-129	-1.0557172826638001e-134	-1.0655702134682184e-134

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	69
1	33	47
done	33	47

end0.0ms

sample1.5s

Algorithm

intervals

Results

555.0ms	7674×	body	80	valid
117.0ms	459×	body	320	valid
113.0ms	514×	body	640	valid
96.0ms	311×	body	1280	valid
25.0ms	264×	body	160	valid
4.0ms	16×	body	2560	valid