Details

sample74.0ms

Algorithm

intervals

Results

38.0ms

361×

body

valid

simplify6.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2434
8	2434
7	2422
6	2265
5	1670
4	779
3	289
2	90
1	27
0	13

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.8b

localize33.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma t (* 9.0 (- z)) (* x y))
6.4b	(/ (fma t (* 9.0 (- z)) (* x y)) (* a 2.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 33

Calls

2 calls:

1.0ms	(fma t (* 9.0 (- z)) (* x y))
12.0ms	(/ (fma t (* 9.0 (- z)) (* x y)) (* a 2.0))

series195.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(fma t (* 9.0 (- z)) (* x y))
100.0ms	(/ (fma t (* 9.0 (- z)) (* x y)) (* a 2.0))

simplify2.7s

Counts

39 → 39

Iterations

Iter	Nodes
done	5001
3	3929
2	507
1	154
0	72

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.4b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* (* (- z) 9.0) t) (* x y))
0.2b	(* (* (- z) 9.0) t)
6.4b	(/ (+ (* (* (- z) 9.0) t) (* x y)) (* a 2.0))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `times-frac` `associate-r` `pow-prod-down` `log1p-expm1-u` `associate-/l*`
2×	`distribute-lft-neg-out` `cbrt-undiv` `flip3-+` `div-exp` `flip-+` `associate-/l/`
1×	`+-commutative` `clear-num` `associate-/r` `sum-log` `fma-def` `frac-2neg` `associate-l` `-commutative` `div-inv`

Counts

3 → 60

Calls

3 calls:

26.0ms	(+ (* (* (- z) 9.0) t) (* x y))
17.0ms	(* (* (- z) 9.0) t)
76.0ms	(/ (+ (* (* (- z) 9.0) t) (* x y)) (* a 2.0))

series220.0ms

Counts

3 → 9

Calls

3 calls:

81.0ms	(+ (* (* (- z) 9.0) t) (* x y))
36.0ms	(* (* (- z) 9.0) t)
102.0ms	(/ (+ (* (* (- z) 9.0) t) (* x y)) (* a 2.0))

simplify1.0s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
2	1699
1	346
0	124

prune533.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- 4.5) (/ t (/ a z)) (/ 0.5 (/ a (* y x))))
0.8b	(/ 0.5 (/ a (* y x)))
3.5b	(/ a (* y x))
6.0b	(/ t (/ a z))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

111×	`times-frac`
64×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
21×	`associate-/r*`
11×	`div-inv`
10×	`cbrt-undiv` `div-exp`
9×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 155

Calls

4 calls:

0.0ms	(fma (- 4.5) (/ t (/ a z)) (/ 0.5 (/ a (* y x))))
26.0ms	(/ 0.5 (/ a (* y x)))
6.0ms	(/ a (* y x))
8.0ms	(/ t (/ a z))

series251.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(fma (- 4.5) (/ t (/ a z)) (/ 0.5 (/ a (* y x))))
52.0ms	(/ 0.5 (/ a (* y x)))
33.0ms	(/ a (* y x))
28.0ms	(/ t (/ a z))

simplify1.2s

Counts

167 → 167

Iterations

Iter	Nodes
done	5001
2	3116
1	702
0	286

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (- 4.5) (* (/ t a) z) (/ 0.5 (/ a (* y x))))
0.8b	(/ 0.5 (/ a (* y x)))
3.5b	(/ a (* y x))
3.9b	(* (/ t a) z)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
35×	`add-sqr-sqrt`
30×	`*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube` `add-exp-log`
13×	`associate-l`
8×	`cbrt-undiv` `associate-/r*` `div-exp`
7×	`div-inv`
6×	`pow1` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`clear-num` `frac-2neg` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `fma-udef`

Counts

4 → 117

Calls

4 calls:

0.0ms	(fma (- 4.5) (* (/ t a) z) (/ 0.5 (/ a (* y x))))
15.0ms	(/ 0.5 (/ a (* y x)))
12.0ms	(/ a (* y x))
18.0ms	(* (/ t a) z)

series288.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(fma (- 4.5) (* (/ t a) z) (/ 0.5 (/ a (* y x))))
37.0ms	(/ 0.5 (/ a (* y x)))
43.0ms	(/ a (* y x))
36.0ms	(* (/ t a) z)

simplify1.0s

Counts

129 → 129

Iterations

Iter	Nodes
done	5002
2	2184
1	485
0	205

prune926.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

Accuracy

32.5% (5.2b remaining)

Error of 5.3b against oracle of 0.0b and baseline of 7.8b

bsearch186.0ms

Steps

Iters	Range		Point
8	64260609.3427585	2139574435580.4946	819283338.3549674
9	-1.9275481642184927e+36	-3.451263932730789e+30	-2.883699790592167e+33

simplify11.0ms

Iterations

Iter	Nodes
done	66
3	66
2	60
1	50
0	39

end0.0ms

sample2.0s

Algorithm

intervals

Results

837.0ms

11298×

body

valid