Details

sample99.0ms

Algorithm

intervals

Results

50.0ms

414×

body

valid

simplify5.0s

Counts

1 → 1

Iterations

Useful iterations: 6 (3.6s)

Iter	Nodes	Cost
0	18	19
1	38	19
2	100	19
3	319	18
4	853	18
5	1819	18
6	3993	16
done	5000	16

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.5b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma y (* x 9.0) b)
0.5b	(- (/ (fma y (* x 9.0) b) z) (* (* a 4.0) t))
1.5b	(/ (fma y (* x 9.0) b) z)
7.6b	(/ (- (/ (fma y (* x 9.0) b) z) (* (* a 4.0) t)) c)

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`fma-neg` `prod-diff`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `diff-log` `div-sub` `fma-udef`

Counts

4 → 111

Calls

4 calls:

0.0ms	(fma y (* x 9.0) b)
27.0ms	(- (/ (fma y (* x 9.0) b) z) (* (* a 4.0) t))
5.0ms	(/ (fma y (* x 9.0) b) z)
76.0ms	(/ (- (/ (fma y (* x 9.0) b) z) (* (* a 4.0) t)) c)

series473.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma y (* x 9.0) b)
208.0ms	(- (/ (fma y (* x 9.0) b) z) (* (* a 4.0) t))
69.0ms	(/ (fma y (* x 9.0) b) z)
161.0ms	(/ (- (/ (fma y (* x 9.0) b) z) (* (* a 4.0) t)) c)

simplify947.0ms

Counts

123 → 123

Iterations

Useful iterations: done (942.0ms)

Iter	Nodes	Cost
0	170	2305
1	378	2243
2	1266	2063
done	5001	1986

prune556.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (* x y) (* z c)) 9.0 (/ b (* z c)))
4.2b	(/ (* (* a 4.0) t) c)
4.2b	(/ b (* z c))
6.5b	(/ (* x y) (* z c))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-exp` `cbrt-unprod`
7×	`times-frac`
5×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
1×	`fma-udef`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma (/ (* x y) (* z c)) 9.0 (/ b (* z c)))
21.0ms	(/ (* (* a 4.0) t) c)
14.0ms	(/ b (* z c))
13.0ms	(/ (* x y) (* z c))

series191.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(fma (/ (* x y) (* z c)) 9.0 (/ b (* z c)))
34.0ms	(/ (* (* a 4.0) t) c)
22.0ms	(/ b (* z c))
31.0ms	(/ (* x y) (* z c))

simplify1.1s

Counts

93 → 93

Iterations

Useful iterations: 2 (275.0ms)

Iter	Nodes	Cost
0	163	1010
1	401	986
2	1907	802
done	5000	802

prune422.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (/ (* x y) (* z c)) 9.0 (/ b (* z c)))
4.2b	(/ b (* z c))
4.5b	(/ (* a 4.0) (/ c t))
6.5b	(/ (* x y) (* z c))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

35×	`times-frac`
33×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`associate-/r*`
12×	`cbrt-undiv` `div-exp`
7×	`prod-exp` `cbrt-unprod`
5×	`div-inv` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`associate-/r/` `fma-udef`

Counts

4 → 104

Calls

4 calls:

1.0ms	(fma (/ (* x y) (* z c)) 9.0 (/ b (* z c)))
16.0ms	(/ b (* z c))
27.0ms	(/ (* a 4.0) (/ c t))
34.0ms	(/ (* x y) (* z c))

series244.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma (/ (* x y) (* z c)) 9.0 (/ b (* z c)))
37.0ms	(/ b (* z c))
57.0ms	(/ (* a 4.0) (/ c t))
57.0ms	(/ (* x y) (* z c))

simplify1.1s

Counts

116 → 116

Iterations

Useful iterations: 2 (339.0ms)

Iter	Nodes	Cost
0	215	1296
1	511	1246
2	2141	1046
done	5000	1046

prune500.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 9.0 (/ (* x y) (* z c)))
4.2b	(/ b (* z c))
4.5b	(/ (* a 4.0) (/ c t))
6.5b	(/ (* x y) (* z c))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-exp-log` `add-cbrt-cube`
36×	`times-frac`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
15×	`associate-/r*`
6×	`pow1` `div-inv`
5×	`associate-r` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
1×	`associate-r/` `pow-prod-down` `associate-/r/` `-commutative` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

48.0ms	(* 9.0 (/ (* x y) (* z c)))
19.0ms	(/ b (* z c))
13.0ms	(/ (* a 4.0) (/ c t))
13.0ms	(/ (* x y) (* z c))

series160.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* 9.0 (/ (* x y) (* z c)))
23.0ms	(/ b (* z c))
51.0ms	(/ (* a 4.0) (/ c t))
34.0ms	(/ (* x y) (* z c))

simplify1.4s

Counts

137 → 137

Iterations

Useful iterations: 2 (514.0ms)

Iter	Nodes	Cost
0	235	1524
1	580	1462
2	2512	1182
done	5000	1182

prune470.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes1.0s

Accuracy

3.5% (10.4b remaining)

Error of 10.6b against oracle of 0.1b and baseline of 10.9b

bsearch418.0ms

Steps

Iters	Range		Point
9	7.520088892128301e+238	1.6770962127106405e+244	1.2723190503240347e+244
7	4.71801383509725e+52	1.3326311595534397e+54	2.9877156437730873e+53
9	2.4885961611920785e-173	4.496029880187708e-166	1.4474005879192812e-170

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	43	93
1	58	76
done	58	76

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.0s

12699×

body

valid