Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

274×

body

valid

simplify35.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	19	15
2	36	15
3	48	15
4	66	15
5	72	15
done	72	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.0b	(- (* b c) (* a d))
27.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 55

Calls

3 calls:

2.0ms	(+ (* c c) (* d d))
2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series152.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (* c c) (* d d))
40.0ms	(- (* b c) (* a d))
85.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.6s

Counts

64 → 64

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	101	1120
1	289	1097
2	1023	981
3	3794	981
done	5000	980

prune174.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 27.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b c) (* a d))
16.1b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
31.6b	(sqrt (+ (* c c) (* d d)))
31.6b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 86

Calls

4 calls:

2.0ms	(- (* b c) (* a d))
10.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series221.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* b c) (* a d))
108.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
34.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.1s

Counts

98 → 98

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	120	1814
1	304	1690
2	855	1590
3	2495	1560
done	5001	1559

prune268.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* c c) (* d d))
17.6b	(/ (* b c) (+ (* c c) (* d d)))
20.0b	(/ (* a d) (+ (* c c) (* d d)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`times-frac` `associate-/r*`
4×	`pow1` `cbrt-undiv` `flip3-+` `div-exp` `associate-/r/` `flip-+`
2×	`+-commutative` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 68

Calls

4 calls:

2.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* c c) (* d d))
6.0ms	(/ (* b c) (+ (* c c) (* d d)))
6.0ms	(/ (* a d) (+ (* c c) (* d d)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (* c c) (* d d))
25.0ms	(+ (* c c) (* d d))
45.0ms	(/ (* b c) (+ (* c c) (* d d)))
43.0ms	(/ (* a d) (+ (* c c) (* d d)))

simplify711.0ms

Counts

80 → 80

Iterations

Useful iterations: 2 (108.0ms)

Iter	Nodes	Cost
0	111	1120
1	306	1096
2	1173	880
done	5002	880

prune195.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 24.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ b (sqrt (+ (* c c) (* d d)))) (/ c (sqrt (+ (* c c) (* d d)))))
20.0b	(/ (* a d) (+ (* c c) (* d d)))
31.6b	(sqrt (+ (* c c) (* d d)))
31.6b	(sqrt (+ (* c c) (* d d)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
51×	`times-frac`
34×	`add-cube-cbrt` `*-un-lft-identity`
30×	`sqrt-prod`
24×	`associate-r` `associate-l`
21×	`add-exp-log` `add-cbrt-cube`
9×	`unswap-sqr`
8×	`pow1` `sqrt-div`
6×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
4×	`add-log-exp`
3×	`associate-/r*` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 130

Calls

4 calls:

40.0ms	(* (/ b (sqrt (+ (* c c) (* d d)))) (/ c (sqrt (+ (* c c) (* d d)))))
6.0ms	(/ (* a d) (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ b (sqrt (+ (* c c) (* d d)))) (/ c (sqrt (+ (* c c) (* d d)))))
42.0ms	(/ (* a d) (+ (* c c) (* d d)))
218.0ms	(sqrt (+ (* c c) (* d d)))
33.0ms	(sqrt (+ (* c c) (* d d)))

simplify840.0ms

Counts

142 → 142

Iterations

Useful iterations: done (836.0ms)

Iter	Nodes	Cost
0	198	3016
1	579	2843
2	2016	2349
done	5000	2299

prune366.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 23.7b

regimes114.0ms

Accuracy

0% (1.3b remaining)

Error of 23.7b against oracle of 22.4b and baseline of 23.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	43
1	18	43
done	18	43

end0.0ms

sample491.0ms

Algorithm

intervals

Results

284.0ms

8491×

body

valid