Details

sample48.0ms

Algorithm

intervals

Results

23.0ms

262×

body

valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(- (* b c) (* a d))
24.3b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite98.0ms

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:

17.0ms	(+ (* c c) (* d d))
16.0ms	(- (* b c) (* a d))
61.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(+ (* c c) (* d d))
56.0ms	(- (* b c) (* a d))
137.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify851.0ms

Counts

64 → 64

Iterations

Useful iterations: done (849.0ms)

Iter	Nodes	Cost
0	101	1120
1	319	1097
2	1746	983
done	5000	981

prune257.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* b c) (* a d))
14.7b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
27.1b	(sqrt (+ (* c c) (* d d)))
27.1b	(sqrt (+ (* c c) (* d d)))

rewrite84.0ms

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:

13.0ms	(- (* b c) (* a d))
37.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
16.0ms	(sqrt (+ (* c c) (* d d)))
16.0ms	(sqrt (+ (* c c) (* d d)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* b c) (* a d))
167.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
50.0ms	(sqrt (+ (* c c) (* d d)))
45.0ms	(sqrt (+ (* c c) (* d d)))

simplify809.0ms

Counts

98 → 98

Iterations

Useful iterations: done (805.0ms)

Iter	Nodes	Cost
0	120	1814
1	312	1682
2	1189	1576
done	5000	1574

prune348.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 21.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.3b	(- (* b c) (* a d))
0.6b	(/ 1 (+ (* c c) (* d d)))
23.8b	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 98

Calls

4 calls:

8.0ms	(+ (* c c) (* d d))
8.0ms	(- (* b c) (* a d))
14.0ms	(/ 1 (+ (* c c) (* d d)))
95.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

series278.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (* c c) (* d d))
62.0ms	(- (* b c) (* a d))
45.0ms	(/ 1 (+ (* c c) (* d d)))
129.0ms	(* (- (* b c) (* a d)) (/ 1 (+ (* c c) (* d d))))

simplify2.3s

Counts

110 → 110

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	140	1797
1	421	1682
2	3051	1431
done	5000	1425

prune268.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 21.3b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (pow d 2) (pow c 2))
0.3b	(- (* b c) (* a d))
24.3b	(/ (- (* b c) (* a d)) (+ (pow d 2) (pow c 2)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
15×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`unpow-prod-down` `distribute-lft-out`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
3×	`pow1` `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 → 65

Calls

3 calls:

20.0ms	(+ (pow d 2) (pow c 2))
8.0ms	(- (* b c) (* a d))
41.0ms	(/ (- (* b c) (* a d)) (+ (pow d 2) (pow c 2)))

series173.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (pow d 2) (pow c 2))
44.0ms	(- (* b c) (* a d))
99.0ms	(/ (- (* b c) (* a d)) (+ (pow d 2) (pow c 2)))

simplify593.0ms

Counts

74 → 74

Iterations

Useful iterations: done (589.0ms)

Iter	Nodes	Cost
0	103	1318
1	287	1251
2	1464	1165
done	5002	1163

prune208.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 21.3b

regimes135.0ms

Accuracy

0% (3.1b remaining)

Error of 26.4b against oracle of 23.4b and baseline of 26.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	25
1	16	25
done	16	25

end0.0ms

sample1.2s

Algorithm

intervals

Results

828.0ms

8444×

body

valid