Details

sample48.0ms

Algorithm

intervals

Results

20.0ms	256×	body	80	valid
8.0ms	256×	pre	80	true

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	22	15
2	48	15
3	102	15
4	205	15
5	387	15
6	831	15
7	3622	15
done	5000	15

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.1b	(* (/ (- x y) (+ (* x x) (* y y))) (+ y x))
18.3b	(/ (- x y) (+ (* x x) (* y y)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `flip3-+` `flip-+` `associate-/l*` `add-log-exp`
4×	`associate-r` `associate-/r/`
3×	`associate-/r*`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip--` `distribute-lft-out`

Counts

3 → 98

Calls

3 calls:

8.0ms	(+ (* x x) (* y y))
90.0ms	(* (/ (- x y) (+ (* x x) (* y y))) (+ y x))
43.0ms	(/ (- x y) (+ (* x x) (* y y)))

series229.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* x x) (* y y))
95.0ms	(* (/ (- x y) (+ (* x x) (* y y))) (+ y x))
83.0ms	(/ (- x y) (+ (* x x) (* y y)))

simplify3.0s

Counts

107 → 107

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	154	1874
1	582	1841
2	3745	1667
done	5001	1663

prune344.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (sqrt (+ (* x x) (* y y))))
0.2b	(* (/ 1 (sqrt (+ (* x x) (* y y)))) (* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (+ y x)))
18.2b	(sqrt (+ (* x x) (* y y)))
18.2b	(sqrt (+ (* x x) (* y y)))

rewrite266.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
52×	`*-un-lft-identity`
48×	`times-frac`
45×	`add-exp-log`
38×	`add-cube-cbrt`
33×	`sqrt-prod`
27×	`add-cbrt-cube`
24×	`associate-l`
20×	`prod-exp`
11×	`pow1` `div-exp`
10×	`cbrt-unprod`
9×	`frac-times` `associate-*r/`
8×	`flip3-+` `sqrt-div` `flip-+`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `associate-/r*`
5×	`associate-/l*`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-/r/` `add-log-exp`
3×	`rec-exp` `1-exp` `pow-prod-down` `associate-*l/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `associate-r` `clear-num` `*-commutative` `flip--`

Counts

4 → 156

Calls

4 calls:

30.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
197.0ms	(* (/ 1 (sqrt (+ (* x x) (* y y)))) (* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (+ y x)))
16.0ms	(sqrt (+ (* x x) (* y y)))
9.0ms	(sqrt (+ (* x x) (* y y)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- x y) (sqrt (+ (* x x) (* y y))))
73.0ms	(* (/ 1 (sqrt (+ (* x x) (* y y)))) (* (/ (- x y) (sqrt (+ (* x x) (* y y)))) (+ y x)))
62.0ms	(sqrt (+ (* x x) (* y y)))
49.0ms	(sqrt (+ (* x x) (* y y)))

simplify3.7s

Counts

168 → 168

Iterations

Useful iterations: 2 (800.0ms)

Iter	Nodes	Cost
0	232	4148
1	719	3831
2	4626	3333
done	5000	3333

prune572.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* (/ (- x y) (+ (* x x) (* y y))) (+ y x)))
0.0b	(log (exp (* (/ (- x y) (+ (* x x) (* y y))) (+ y x))))
0.1b	(* (/ (- x y) (+ (* x x) (* y y))) (+ y x))
18.3b	(/ (- x y) (+ (* x x) (* y y)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
31×	`times-frac`
25×	`add-cube-cbrt`
21×	`associate-l`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
5×	`log-prod` `associate-/l*`
4×	`flip3-+` `associate-r` `exp-sum` `associate-/r/` `flip-+`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-/r*` `log-pow`
2×	`cbrt-undiv` `frac-times` `exp-prod` `exp-to-pow` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `div-sub` `rem-log-exp` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `rem-exp-log` `distribute-lft-out`

Counts

4 → 115

Calls

4 calls:

13.0ms	(exp (* (/ (- x y) (+ (* x x) (* y y))) (+ y x)))
10.0ms	(log (exp (* (/ (- x y) (+ (* x x) (* y y))) (+ y x))))
98.0ms	(* (/ (- x y) (+ (* x x) (* y y))) (+ y x))
40.0ms	(/ (- x y) (+ (* x x) (* y y)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(exp (* (/ (- x y) (+ (* x x) (* y y))) (+ y x)))
82.0ms	(log (exp (* (/ (- x y) (+ (* x x) (* y y))) (+ y x))))
78.0ms	(* (/ (- x y) (+ (* x x) (* y y))) (+ y x))
97.0ms	(/ (- x y) (+ (* x x) (* y y)))

simplify2.2s

Counts

127 → 127

Iterations

Useful iterations: 2 (524.0ms)

Iter	Nodes	Cost
0	175	2345
1	587	2271
2	3404	2052
done	5001	2052

prune526.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(exp (/ (* (+ y x) (- x y)) (+ (* x x) (* y y))))
0.0b	(log (exp (/ (* (+ y x) (- x y)) (+ (* x x) (* y y)))))
19.2b	(/ (* (+ y x) (- x y)) (+ (* x x) (* y y)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

18×	`exp-prod`
11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`log-pow`
9×	`add-exp-log` `times-frac` `add-cbrt-cube`
8×	`associate-/l/`
7×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-/r/`
5×	`pow1`
4×	`frac-times`
3×	`log-prod` `flip3--` `associate-/r*` `flip--` `div-inv`
2×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/`
1×	`+-commutative` `frac-2neg` `rem-log-exp` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `rem-exp-log` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

8.0ms	(+ (* x x) (* y y))
32.0ms	(exp (/ (* (+ y x) (- x y)) (+ (* x x) (* y y))))
52.0ms	(log (exp (/ (* (+ y x) (- x y)) (+ (* x x) (* y y)))))
45.0ms	(/ (* (+ y x) (- x y)) (+ (* x x) (* y y)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* x x) (* y y))
129.0ms	(exp (/ (* (+ y x) (- x y)) (+ (* x x) (* y y))))
83.0ms	(log (exp (/ (* (+ y x) (- x y)) (+ (* x x) (* y y)))))
106.0ms	(/ (* (+ y x) (- x y)) (+ (* x x) (* y y)))

simplify1.6s

Counts

92 → 92

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	132	1611
1	406	1536
2	2794	1307
done	5000	1303

prune405.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes112.0ms

Accuracy

77.1% (4.6b remaining)

Error of 5.1b against oracle of 0.5b and baseline of 20.6b

bsearch189.0ms

Steps

Iters	Range		Point
8	7.640585338783926e-164	2.7595611295545184e-161	2.495375493781524e-161
9	-6.745320625753358e-188	-1.6101478087962774e-193	-6.64036774862504e-188
9	-2.2926673522997828e-157	-6.571498772207673e-163	-6.671301972241294e-163
8	-6.888726652681395e+154	-1.350243324689865e+150	-5.351376453551335e+150

simplify11.0ms

Iterations

Useful iterations: done (10.0ms)

Iter	Nodes	Cost
0	29	59
1	35	58
done	35	57

end0.0ms

sample1.2s

Algorithm

intervals

Results

664.0ms	8000×	body	80	valid
246.0ms	8000×	pre	80	true