Details

sample25.0ms

Algorithm

intervals

Results

12.0ms

274×

body

valid

simplify42.0ms

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize26.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (* b c) (* a d))
24.7b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 44

Calls

2 calls:

10.0ms	(- (* b c) (* a d))
21.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series156.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (* b c) (* a d))
106.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify2.1s

Counts

50 → 50

Iterations

Iter	Nodes
done	5001
3	4329
2	980
1	254
0	86

prune304.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 24.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
15.4b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
28.7b	(sqrt (+ (* c c) (* d d)))
28.7b	(sqrt (+ (* c c) (* d d)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

10.0ms	(- (* b c) (* a d))
46.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
13.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- (* b c) (* a d))
206.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
70.0ms	(sqrt (+ (* c c) (* d d)))
63.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1128
1	308
0	118

prune640.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 21.6b

localize20.0ms

Local error

Found 3 expressions with local error:

0.5b	(- (* b c) (* a d))
1.3b	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
23.8b	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 127

Calls

3 calls:

6.0ms	(- (* b c) (* a d))
32.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
34.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(- (* b c) (* a d))
160.0ms	(/ 1 (/ (+ (* c c) (* d d)) (- (* b c) (* a d))))
81.0ms	(/ (+ (* c c) (* d d)) (- (* b c) (* a d)))

simplify1.7s

Counts

136 → 136

Iterations

Iter	Nodes
done	5002
2	2790
1	533
0	192

prune709.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (- (* b c) (* a d)))
0.5b	(- (* b c) (* a d))
1.3b	(/ 1 (* (+ (* c c) (* d d)) (/ 1 (- (* b c) (* a d)))))
24.1b	(* (+ (* c c) (* d d)) (/ 1 (- (* b c) (* a d))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log`
29×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube` `div-exp`
16×	`prod-exp`
15×	`associate-r`
10×	`pow1` `rec-exp` `1-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*` `add-log-exp`
4×	`frac-times` `associate-/r` `flip3-+` `associate-l/` `cbrt-unprod` `flip-+`
3×	`flip3--` `associate-l` `div-inv` `pow-flip` `flip--` `unswap-sqr`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*r/` `un-div-inv` `inv-pow`
1×	`sub-neg` `diff-log` `*-commutative`

Counts

4 → 131

Calls

4 calls:

13.0ms	(/ 1 (- (* b c) (* a d)))
6.0ms	(- (* b c) (* a d))
42.0ms	(/ 1 (* (+ (* c c) (* d d)) (/ 1 (- (* b c) (* a d)))))
66.0ms	(* (+ (* c c) (* d d)) (/ 1 (- (* b c) (* a d))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1 (- (* b c) (* a d)))
57.0ms	(- (* b c) (* a d))
171.0ms	(/ 1 (* (+ (* c c) (* d d)) (/ 1 (- (* b c) (* a d)))))
77.0ms	(* (+ (* c c) (* d d)) (/ 1 (- (* b c) (* a d))))

simplify2.9s

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	3880
1	513
0	169

prune504.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 21.6b

regimes265.0ms

Accuracy

-8.3% (3.5b remaining)

Error of 26.2b against oracle of 22.7b and baseline of 25.9b

bsearch48.0ms

Steps

Iters	Range		Point
9	2.0782291391057034e+47	1.0561172955237832e+55	1.0408011483354069e+55

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

792.0ms

8465×

body

valid