Details

sample89.0ms

Algorithm

intervals

Results

59.0ms

669×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	25	17
2	40	17
3	66	17
4	120	17
5	426	17
6	3507	17
done	5001	17

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
3×	`unpow-prod-down` `pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr` `sqr-pow`

Counts

4 → 58

Calls

4 calls:

26.0ms	(* 4.0 (* b b))
8.0ms	(+ (* a a) (* b b))
85.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
17.0ms	(pow (+ (* a a) (* b b)) 2.0)

series366.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 4.0 (* b b))
53.0ms	(+ (* a a) (* b b))
101.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
183.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: 2 (448.0ms)

Iter	Nodes	Cost
0	117	931
1	385	848
2	2107	778
done	5003	778

prune259.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
2.1b	(* (pow a 2) (pow b 2))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-exp-log`
28×	`prod-exp`
24×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`add-cbrt-cube` `unpow2` `sqr-pow`
9×	`associate-r`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-log-exp`
4×	`cbrt-unprod`
2×	`pow-prod-down` `*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

3 → 87

Calls

3 calls:

28.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
29.0ms	(* 2 (* (pow a 2) (pow b 2)))
36.0ms	(* (pow a 2) (pow b 2))

series172.0ms

Counts

3 → 9

Calls

3 calls:

79.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
43.0ms	(* 2 (* (pow a 2) (pow b 2)))
50.0ms	(* (pow a 2) (pow b 2))

simplify1.7s

Counts

96 → 96

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	122	1229
1	309	1074
2	1948	886
done	5000	876

prune292.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow b 4) (* 2 (* (* (fabs b) (* a a)) (sqrt (pow b 2)))))
0.6b	(* (* (fabs b) (* a a)) (sqrt (pow b 2)))
0.9b	(* (fabs b) (* a a))
21.3b	(sqrt (pow b 2))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
16×	`sqrt-prod`
13×	`add-sqr-sqrt`
12×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`unpow-prod-down`
6×	`add-log-exp`
4×	`rem-sqrt-square` `associate-l`
3×	`unpow2` `sqr-pow`
2×	`*-commutative`
1×	`+-commutative` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip-+` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

21.0ms	(+ (pow b 4) (* 2 (* (* (fabs b) (* a a)) (sqrt (pow b 2)))))
105.0ms	(* (* (fabs b) (* a a)) (sqrt (pow b 2)))
17.0ms	(* (fabs b) (* a a))
6.0ms	(sqrt (pow b 2))

series149.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ (pow b 4) (* 2 (* (* (fabs b) (* a a)) (sqrt (pow b 2)))))
52.0ms	(* (* (fabs b) (* a a)) (sqrt (pow b 2)))
34.0ms	(* (fabs b) (* a a))
10.0ms	(sqrt (pow b 2))

simplify1.9s

Counts

92 → 92

Iterations

Useful iterations: 2 (371.0ms)

Iter	Nodes	Cost
0	123	1151
1	353	1045
2	2306	790
done	5001	790

prune416.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(* 4.0 (* b b))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
2.1b	(* (pow a 2) (pow b 2))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `associate-l`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unpow2` `sqr-pow`
9×	`add-log-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 108

Calls

4 calls:

39.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
17.0ms	(* 4.0 (* b b))
95.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
26.0ms	(* (pow a 2) (pow b 2))

series258.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
45.0ms	(* 4.0 (* b b))
111.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
50.0ms	(* (pow a 2) (pow b 2))

simplify2.4s

Counts

120 → 120

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	160	1554
1	432	1418
2	2802	1118
done	5002	1106

prune351.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

97.4% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.0b

bsearch124.0ms

Steps

Iters	Range		Point
7	2.9878765326228963e-24	1.070232290204598e-22	5.8287091483034594e-24
6	-0.00015980627971116164	-2.0664971820228305e-05	-8.880624384766911e-05

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	33	75
1	46	53
done	46	53

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.2s

20565×

body

valid