Details

sample62.0ms

Algorithm

intervals

Results

22.0ms	236×	body	80	valid
5.0ms	19×	body	320	valid
5.0ms	14×	body	640	valid
3.0ms	8×	body	1280	valid
2.0ms	14×	body	160	valid

simplify9.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (31.0ms)

Iter	Nodes	Cost
0	11	13
1	20	13
2	45	13
3	116	12
4	322	12
5	770	12
6	1556	12
7	2865	12
8	4698	12
done	5000	12

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
16.0b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite44.0ms

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:

39.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series278.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(/ (- y x) (- a t))
180.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	118	918
1	270	890
2	658	838
3	1740	836
done	5000	830

prune369.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
4.9b	(* (/ (- y x) (- a t)) (- z t))
5.2b	(+ (* (/ (- y x) (- a t)) (- z t)) x)

rewrite197.0ms

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:

33.0ms	(/ (- y x) (- a t))
91.0ms	(* (/ (- y x) (- a t)) (- z t))
64.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)

series748.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms	(/ (- y x) (- a t))
348.0ms	(* (/ (- y x) (- a t)) (- z t))
284.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)

simplify1.6s

Counts

179 → 179

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	256	3107
1	667	2740
2	1944	2516
done	5000	2490

prune818.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
0.8b	(* (/ (cbrt (- y x)) (- a t)) (- z t))
0.9b	(* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t)))
9.1b	(+ (* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t))) x)

rewrite514.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
99×	`distribute-rgt-in` `distribute-lft-in`
90×	`prod-diff`
87×	`add-cube-cbrt`
66×	`add-exp-log`
53×	`associate-l`
45×	`times-frac`
44×	`associate-+l+`
35×	`add-cbrt-cube`
33×	`prod-exp`
31×	`cbrt-prod`
20×	`cbrt-unprod`
18×	`div-exp`
15×	`distribute-lft-out--` `difference-of-squares`
11×	`pow1` `frac-times` `associate-*r/`
10×	`cbrt-undiv` `sub-neg`
8×	`flip3--` `flip--`
6×	`1-exp` `associate-r` `add-log-exp`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*l/` `log1p-expm1-u`
3×	`unswap-sqr`
2×	`cbrt-div` `associate-/r/` `*-commutative` `div-inv`
1×	`+-commutative` `fma-def` `flip3-+` `pow1/3` `sum-log` `flip-+`

Counts

4 → 270

Calls

4 calls:

4.0ms	(cbrt (- y x))
120.0ms	(* (/ (cbrt (- y x)) (- a t)) (- z t))
180.0ms	(* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t)))
192.0ms	(+ (* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t))) x)

series1.8s

Counts

4 → 12

Calls

4 calls:

236.0ms	(cbrt (- y x))
960.0ms	(* (/ (cbrt (- y x)) (- a t)) (- z t))
305.0ms	(* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t)))
263.0ms	(+ (* (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t))) x)

simplify2.8s

Counts

282 → 282

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	427	8760
1	1088	7413
2	3435	5128
done	5000	4397

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y x))
0.5b	(cbrt (- y x))
0.8b	(* (/ (cbrt (- y x)) (- a t)) (- z t))
12.6b	(fma (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t)) x)

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
46×	`associate-l`
42×	`times-frac`
38×	`add-cube-cbrt`
36×	`cbrt-prod`
18×	`prod-diff`
16×	`distribute-lft-out--` `difference-of-squares`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-exp-log`
8×	`add-cbrt-cube`
6×	`pow1`
5×	`flip3--` `associate-r` `flip--`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `pow1/3` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 140

Calls

4 calls:

4.0ms	(cbrt (- y x))
4.0ms	(cbrt (- y x))
104.0ms	(* (/ (cbrt (- y x)) (- a t)) (- z t))
1.0ms	(fma (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t)) x)

series2.0s

Counts

4 → 12

Calls

4 calls:

262.0ms	(cbrt (- y x))
207.0ms	(cbrt (- y x))
843.0ms	(* (/ (cbrt (- y x)) (- a t)) (- z t))
669.0ms	(fma (/ (* (cbrt (- y x)) (cbrt (- y x))) 1) (* (/ (cbrt (- y x)) (- a t)) (- z t)) x)

simplify1.4s

Counts

152 → 152

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	277	2800
1	665	2580
2	1849	2277
done	5000	2169

prune881.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.0b

regimes493.0ms

Accuracy

-16.8% (6.9b remaining)

Error of 13.5b against oracle of 6.6b and baseline of 12.5b

bsearch149.0ms

Steps

Iters	Range		Point
4	5.167707146549307e-240	9.55766236861509e-240	6.128009851376196e-240
9	-8.835946115642157e-259	-8.700459885676303e-264	-1.825612937156263e-263

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	59
1	27	33
done	27	33

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	7767×	body	80	valid
200.0ms	281×	body	1280	valid
188.0ms	493×	body	640	valid
76.0ms	363×	body	320	valid
38.0ms	273×	body	160	valid
8.0ms	19×	body	2560	valid