Details

sample107.0ms

Algorithm

intervals

Results

84.0ms

695×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
6	3490
5	1450
4	532
3	149
2	53
1	28
0	12

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (* a a) (* b b))
0.0b	(* (* b b) 4)
0.4b	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-r`
4×	`frac-times` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`swap-sqr`
2×	`+-commutative` `sum-log` `associate-l/` `associate-r/` `*-commutative` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `distribute-lft-in` `pow-plus` `pow-sqr` `pow-prod-up`

Counts

4 → 80

Calls

4 calls:

15.0ms	(+ (* a a) (* b b))
15.0ms	(+ (* a a) (* b b))
32.0ms	(* (* b b) 4)
40.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))

series190.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ (* a a) (* b b))
50.0ms	(+ (* a a) (* b b))
49.0ms	(* (* b b) 4)
54.0ms	(* (+ (* a a) (* b b)) (+ (* a a) (* b b)))

simplify2.5s

Counts

92 → 92

Iterations

Iter	Nodes
3	5783
2	1431
1	372
0	108

prune809.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))
0.2b	(* (sqrt (+ (* a a) (* b b))) (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))
8.2b	(sqrt (+ (* a a) (* b b)))
8.2b	(sqrt (+ (* a a) (* b b)))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

46×	`sqrt-div`
35×	`flip3-+` `flip-+`
32×	`frac-times`
30×	`pow1`
19×	`add-sqr-sqrt`
16×	`associate-*r/`
15×	`pow-prod-up`
13×	`sqrt-prod`
12×	`sqrt-pow1` `pow1/2` `associate-l`
11×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`associate-*l/`
6×	`pow-plus`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `cube-unmult` `*-commutative` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

58.0ms	(* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))
132.0ms	(* (sqrt (+ (* a a) (* b b))) (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))
12.0ms	(sqrt (+ (* a a) (* b b)))
12.0ms	(sqrt (+ (* a a) (* b b)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b)))
62.0ms	(* (sqrt (+ (* a a) (* b b))) (* (sqrt (+ (* a a) (* b b))) (+ (* a a) (* b b))))
49.0ms	(sqrt (+ (* a a) (* b b)))
66.0ms	(sqrt (+ (* a a) (* b b)))

simplify814.0ms

Counts

143 → 143

Iterations

Iter	Nodes
2	2292
1	546
0	166

prune1.7s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ (* a a) (* b b))) 4)
0.0b	(+ (* a a) (* b b))
0.0b	(* (* b b) 4)
8.2b	(sqrt (+ (* a a) (* b b)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-sqr-sqrt`
10×	`add-exp-log`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
6×	`unpow-prod-down` `sqrt-prod` `add-log-exp`
4×	`insert-posit16`
3×	`pow-unpow` `pow-pow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sqrt-pow1` `flip3-+` `pow1/2` `sqrt-div` `flip-+`
1×	`pow-to-exp` `+-commutative` `rem-sqrt-square` `sum-log` `associate-l` `pow-exp` `*-commutative` `sqrt-pow2` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

8.0ms	(pow (sqrt (+ (* a a) (* b b))) 4)
7.0ms	(+ (* a a) (* b b))
15.0ms	(* (* b b) 4)
18.0ms	(sqrt (+ (* a a) (* b b)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(pow (sqrt (+ (* a a) (* b b))) 4)
51.0ms	(+ (* a a) (* b b))
39.0ms	(* (* b b) 4)
42.0ms	(sqrt (+ (* a a) (* b b)))

simplify2.3s

Counts

84 → 84

Iterations

Iter	Nodes
3	2989
2	1055
1	303
0	116

prune808.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize93.0ms

Local error

Found 4 expressions with local error:

10.2b	(sqrt (+ (* (* b b) (- (* b b) (* a a))) (* (* a a) (* a a))))
14.6b	(sqrt (* (+ (* a a) (* b b)) (- (* a a) (* b b))))
17.7b	(/ (* (* (+ (* a a) (* b b)) (sqrt (* (+ (* a a) (* b b)) (- (* a a) (* b b))))) (sqrt (+ (* (* a (* a a)) (* a (* a a))) (* (* b (* b b)) (* b (* b b)))))) (* (sqrt (- (* a a) (* b b))) (sqrt (+ (* (* b b) (- (* b b) (* a a))) (* (* a a) (* a a))))))
18.9b	(sqrt (+ (* (* a (* a a)) (* a (* a a))) (* (* b (* b b)) (* b (* b b)))))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

150×	`sqrt-div`
144×	`frac-times`
89×	`flip3-+` `flip-+`
80×	`associate-/l/`
54×	`associate-*l/`
48×	`associate-*r/`
33×	`flip3--` `flip--`
25×	`add-cbrt-cube` `add-exp-log`
9×	`pow1` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `associate-/r/` `sqrt-prod`
6×	`cbrt-undiv` `*-un-lft-identity` `div-exp` `add-cube-cbrt`
4×	`sqrt-pow1` `cube-unmult` `insert-posit16` `add-log-exp`
3×	`pow1/2` `pow-prod-down`
2×	`rem-sqrt-square`
1×	`clear-num` `associate-/r` `frac-2neg` `times-frac` `sum-cubes` `div-inv` `associate-/l`

Counts

4 → 167

Calls

4 calls:

67.0ms	(sqrt (+ (* (* b b) (- (* b b) (* a a))) (* (* a a) (* a a))))
28.0ms	(sqrt (* (+ (* a a) (* b b)) (- (* a a) (* b b))))
535.0ms	(/ (* (* (+ (* a a) (* b b)) (sqrt (* (+ (* a a) (* b b)) (- (* a a) (* b b))))) (sqrt (+ (* (* a (* a a)) (* a (* a a))) (* (* b (* b b)) (* b (* b b)))))) (* (sqrt (- (* a a) (* b b))) (sqrt (+ (* (* b b) (- (* b b) (* a a))) (* (* a a) (* a a))))))
486.0ms	(sqrt (+ (* (* a (* a a)) (* a (* a a))) (* (* b (* b b)) (* b (* b b)))))

series605.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt (+ (* (* b b) (- (* b b) (* a a))) (* (* a a) (* a a))))
130.0ms	(sqrt (* (+ (* a a) (* b b)) (- (* a a) (* b b))))
239.0ms	(/ (* (* (+ (* a a) (* b b)) (sqrt (* (+ (* a a) (* b b)) (- (* a a) (* b b))))) (sqrt (+ (* (* a (* a a)) (* a (* a a))) (* (* b (* b b)) (* b (* b b)))))) (* (sqrt (- (* a a) (* b b))) (sqrt (+ (* (* b b) (- (* b b) (* a a))) (* (* a a) (* a a))))))
125.0ms	(sqrt (+ (* (* a (* a a)) (* a (* a a))) (* (* b (* b b)) (* b (* b b)))))

simplify3.3s

Counts

179 → 179

Iterations

Iter	Nodes
2	5615
1	1249
0	366

prune4.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	17
1	17
0	12

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.9s

20466×

body

valid