Details

sample41.0ms

Algorithm

intervals

Results

26.0ms

691×

body

valid

simplify4.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	25	17
2	39	17
3	63	17
4	109	17
5	246	17
6	931	17
7	4543	17
done	5000	17

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

2.0ms	(+ (* a a) (* b b))
6.0ms	(* 4.0 (* b b))
22.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
6.0ms	(pow (+ (* a a) (* b b)) 2.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a a) (* b b))
27.0ms	(* 4.0 (* b b))
66.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.5s

Counts

70 → 70

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	117	931
1	318	838
2	1106	778
3	4839	778
done	5000	778

prune164.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
19.0b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.0b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

37.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series602.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0)))
149.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
151.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
148.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify1.5s

Counts

121 → 121

Iterations

Useful iterations: 3 (505.0ms)

Iter	Nodes	Cost
0	119	2918
1	208	2763
2	600	2621
3	2487	2425
done	5000	2425

prune371.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize13.0ms

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)))
2.3b	(* (pow a 2) (pow b 2))

rewrite28.0ms

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:

6.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
10.0ms	(* 2 (* (pow a 2) (pow b 2)))
9.0ms	(* (pow a 2) (pow b 2))

series128.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms	(* 2 (* (pow a 2) (pow b 2)))
36.0ms	(* (pow a 2) (pow b 2))

simplify662.0ms

Counts

96 → 96

Iterations

Useful iterations: done (659.0ms)

Iter	Nodes	Cost
0	122	1229
1	298	1062
2	1274	884
done	5001	882

prune196.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* 4.0 4.0) (pow b 4))
0.3b	(pow (+ (* a a) (* b b)) (* 2 2.0))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
35.3b	(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 4.0) (pow b 4))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-cbrt-cube`
10×	`unpow-prod-down`
9×	`times-frac` `prod-exp`
7×	`associate-r`
6×	`pow1`
4×	`pow-to-exp` `pow-unpow` `pow-exp` `add-log-exp` `sqr-pow`
3×	`associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`flip3--` `pow-pow` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `associate-l` `clear-num` `*-commutative` `div-inv`

Counts

4 → 91

Calls

4 calls:

10.0ms	(* (* 4.0 4.0) (pow b 4))
4.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
90.0ms	(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 4.0) (pow b 4))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series470.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 4.0 4.0) (pow b 4))
107.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)
219.0ms	(/ (- (pow (+ (* a a) (* b b)) (* 2 2.0)) (* (* 4.0 4.0) (pow b 4))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify883.0ms

Counts

103 → 103

Iterations

Useful iterations: 2 (265.0ms)

Iter	Nodes	Cost
0	201	2629
1	493	2517
2	2065	2313
done	5000	2313

prune330.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes124.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	15	17
done	15	17

end0.0ms

sample1.1s

Algorithm

intervals

Results

777.0ms

21017×

body

valid