Details

sample78.0ms

Algorithm

intervals

Results

46.0ms

627×

body

valid

simplify5.2s

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	118	17
5	255	17
6	849	17
7	3688	17
done	5000	17

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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:

61.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
8.0ms	(+ (* a a) (* b b))
18.0ms	(* 4.0 (* b b))
15.0ms	(pow (+ (* a a) (* b b)) 2.0)

series328.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
34.0ms	(+ (* a a) (* b b))
54.0ms	(* 4.0 (* b b))
149.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.8s

Counts

70 → 70

Iterations

Useful iterations: 2 (260.0ms)

Iter	Nodes	Cost
0	117	931
1	311	838
2	943	778
3	2981	778
done	5001	778

prune207.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
13.5b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
13.5b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
13.5b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

357.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
53.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
40.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
43.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series1.1s

Counts

4 → 12

Calls

4 calls:

249.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
277.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
273.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
302.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify2.0s

Counts

99 → 99

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	121	3626
1	263	3291
2	718	3029
3	1968	2636
done	5000	2592

prune400.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 2 (* (pow a 2) (pow b 2)))
1.2b	(* (pow a 2) (pow b 2))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-exp-log`
28×	`prod-exp`
23×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`associate-l`
10×	`unpow2` `sqr-pow`
9×	`associate-r` `add-cbrt-cube`
7×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `cbrt-unprod`
2×	`pow-prod-down` `*-commutative` `add-log-exp`

Counts

2 → 76

Calls

2 calls:

49.0ms	(* 2 (* (pow a 2) (pow b 2)))
18.0ms	(* (pow a 2) (pow b 2))

series134.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(* 2 (* (pow a 2) (pow b 2)))
66.0ms	(* (pow a 2) (pow b 2))

simplify4.8s

Counts

82 → 82

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	100	937
1	227	811
2	704	649
3	3729	641
done	5000	617

prune232.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(* 4.0 (* b b))
1.2b	(* (pow a 2) (pow b 2))

rewrite172.0ms

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:

84.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
42.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
20.0ms	(* 4.0 (* b b))
22.0ms	(* (pow a 2) (pow b 2))

series216.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
53.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
34.0ms	(* 4.0 (* b b))
35.0ms	(* (pow a 2) (pow b 2))

simplify1.2s

Counts

120 → 120

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	160	1554
1	385	1400
2	1327	1118
done	5000	1094

prune385.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	52
1	19	52
done	19	52

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.0s

20344×

body

valid