Details

sample24.0ms

Algorithm

intervals

Results

12.0ms

272×

body

valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	15
1	15	15
done	15	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
27.9b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

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`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series151.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
86.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify1.6s

Counts

62 → 62

Iterations

Useful iterations: 3 (520.0ms)

Iter	Nodes	Cost
0	98	1090
1	270	1067
2	931	965
3	3229	951
done	5001	951

prune205.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 27.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (* a c) (* b d))
16.8b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
31.1b	(sqrt (+ (* c c) (* d d)))
31.1b	(sqrt (+ (* c c) (* d d)))

rewrite23.0ms

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`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

2.0ms	(+ (* a c) (* b d))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* a c) (* b d))
117.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
43.0ms	(sqrt (+ (* c c) (* d d)))
39.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

96 → 96

Iterations

Useful iterations: 3 (353.0ms)

Iter	Nodes	Cost
0	116	1780
1	274	1657
2	752	1557
3	2017	1527
done	5000	1527

prune319.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 24.4b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.7b	(+ (* a c) (* b d))
27.9b	(/ (* 1 (+ (* a c) (* b d))) (+ (* c c) (* d d)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 48

Calls

3 calls:

2.0ms	(+ (* c c) (* d d))
2.0ms	(+ (* a c) (* b d))
8.0ms	(/ (* 1 (+ (* a c) (* b d))) (+ (* c c) (* d d)))

series148.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (* c c) (* d d))
34.0ms	(+ (* a c) (* b d))
86.0ms	(/ (* 1 (+ (* a c) (* b d))) (+ (* c c) (* d d)))

simplify3.0s

Counts

57 → 57

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	101	959
1	316	885
2	1203	753
3	4986	739
done	5000	739

prune154.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 24.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.2b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
0.7b	(+ (* a c) (* b d))
27.8b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

2.0ms	(+ (* c c) (* d d))
10.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
2.0ms	(+ (* a c) (* b d))
10.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (* c c) (* d d))
148.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
34.0ms	(+ (* a c) (* b d))
56.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify887.0ms

Counts

149 → 149

Iterations

Useful iterations: 2 (284.0ms)

Iter	Nodes	Cost
0	206	3676
1	518	3470
2	1605	3111
done	5000	3111

prune291.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 24.4b

regimes167.0ms

Accuracy

-11% (3.3b remaining)

Error of 26.9b against oracle of 23.6b and baseline of 26.5b

bsearch83.0ms

Steps

Iters	Range		Point
8	7.2003153639421815e+143	1.3871548251723246e+147	1.3021609369269456e+147
9	4.0573096534452066e+47	2.7287424349260767e+55	2.666479014498774e+55

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	60
1	29	60
done	29	60

end0.0ms

sample554.0ms

Algorithm

intervals

Results

318.0ms

8471×

body

valid