Details

sample46.0ms

Algorithm

intervals

Results

23.0ms

271×

body

valid

simplify113.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	94
6	94
5	90
4	76
3	56
2	40
1	21
0	11

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.5b	(- (* b c) (* a d))
30.9b	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-cbrt-cube` `add-exp-log`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l`
2×	`flip3-+` `flip3--` `associate-/r/` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `sub-neg` `fma-def` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

3 → 64

Calls

3 calls:

6.0ms	(+ (* c c) (* d d))
7.0ms	(- (* b c) (* a d))
45.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series278.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(+ (* c c) (* d d))
73.0ms	(- (* b c) (* a d))
154.0ms	(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify1.5s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1783
1	335
0	110

prune491.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 30.6b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
17.6b	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
33.8b	(sqrt (+ (* c c) (* d d)))
33.8b	(sqrt (+ (* c c) (* d d)))

rewrite90.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 98

Calls

4 calls:

12.0ms	(- (* b c) (* a d))
49.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
12.0ms	(sqrt (+ (* c c) (* d d)))
12.0ms	(sqrt (+ (* c c) (* d d)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b c) (* a d))
192.0ms	(/ (- (* b c) (* a d)) (sqrt (+ (* c c) (* d d))))
66.0ms	(sqrt (+ (* c c) (* d d)))
64.0ms	(sqrt (+ (* c c) (* d d)))

simplify1.4s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1257
1	334
0	129

prune797.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 28.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma c c (* d d))
0.5b	(- (* b c) (* a d))
0.7b	(/ 1 (fma c c (* d d)))
30.2b	(* (- (* b c) (* a d)) (/ 1 (fma c c (* d d))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`times-frac` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `log1p-expm1-u`
3×	`associate-/r` `flip3--` `associate-l` `flip--` `associate-/l` `unswap-sqr`
2×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma c c (* d d))
7.0ms	(- (* b c) (* a d))
4.0ms	(/ 1 (fma c c (* d d)))
39.0ms	(* (- (* b c) (* a d)) (/ 1 (fma c c (* d d))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma c c (* d d))
55.0ms	(- (* b c) (* a d))
58.0ms	(/ 1 (fma c c (* d d)))
141.0ms	(* (- (* b c) (* a d)) (/ 1 (fma c c (* d d))))

simplify1.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1781
1	312
0	134

prune677.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 28.4b

localize84.0ms

Local error

Found 4 expressions with local error:

33.8b	(sqrt (+ (* c c) (* d d)))
34.9b	(cbrt (+ (* c c) (* d d)))
34.9b	(cbrt (+ (* c c) (* d d)))
34.9b	(cbrt (+ (* c c) (* d d)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`

Counts

4 → 63

Calls

4 calls:

6.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))
4.0ms	(cbrt (+ (* c c) (* d d)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt (+ (* c c) (* d d)))
107.0ms	(cbrt (+ (* c c) (* d d)))
135.0ms	(cbrt (+ (* c c) (* d d)))
126.0ms	(cbrt (+ (* c c) (* d d)))

simplify2.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
3	3440
2	583
1	162
0	69

prune608.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 28.4b

regimes511.0ms

Accuracy

0% (3.2b remaining)

Error of 26.9b against oracle of 23.7b and baseline of 26.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

1.0s

8480×

body

valid