Details

sample41.0ms

Algorithm

intervals

Results

16.0ms	283×	body	80	valid
4.0ms	81×	body	80	nan

simplify71.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	118
5	118
4	97
3	72
2	46
1	22
0	12

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.7b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma z z (- (* a t)))
2.5b	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
9.0b	(/ (* z y) (sqrt (fma z z (- (* a t)))))
23.2b	(sqrt (fma z z (- (* a t))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac` `sqrt-prod`
10×	`associate-l`
7×	`pow1`
6×	`associate-/r*`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `associate-/l*` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma z z (- (* a t)))
44.0ms	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
15.0ms	(/ (* z y) (sqrt (fma z z (- (* a t)))))
2.0ms	(sqrt (fma z z (- (* a t))))

series432.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(fma z z (- (* a t)))
149.0ms	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
99.0ms	(/ (* z y) (sqrt (fma z z (- (* a t)))))
116.0ms	(sqrt (fma z z (- (* a t))))

simplify1.0s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1731
1	312
0	130

prune757.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize61.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma z z (- (* a t)))
4.8b	(* (/ z (sqrt (sqrt (fma z z (- (* a t)))))) (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (fma z z (- (* a t))))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
42×	`add-sqr-sqrt`
39×	`times-frac`
31×	`associate-l`
29×	`*-un-lft-identity` `add-cube-cbrt`
25×	`add-cbrt-cube` `add-exp-log`
15×	`associate-r`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`sqrt-div`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `associate-/r/` `div-inv` `flip--`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `fma-udef`

Counts

4 → 118

Calls

4 calls:

0.0ms	(fma z z (- (* a t)))
109.0ms	(* (/ z (sqrt (sqrt (fma z z (- (* a t)))))) (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))))
8.0ms	(sqrt (- (* z z) (* t a)))
1.0ms	(sqrt (fma z z (- (* a t))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma z z (- (* a t)))
284.0ms	(* (/ z (sqrt (sqrt (fma z z (- (* a t)))))) (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))))
109.0ms	(sqrt (- (* z z) (* t a)))
130.0ms	(sqrt (fma z z (- (* a t))))

simplify1.6s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	3256
1	622
0	222

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.2b	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
2.5b	(* (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)) x)
23.2b	(sqrt (- (* z z) (* t a)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

726×	`times-frac`
371×	`add-sqr-sqrt`
342×	`*-un-lft-identity`
338×	`add-cube-cbrt`
215×	`associate-l`
122×	`sqrt-prod`
41×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`associate-/l*`
18×	`div-exp` `div-inv`
10×	`prod-exp`
9×	`cbrt-undiv` `unswap-sqr`
7×	`pow1`
6×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`rec-exp` `associate-/r` `1-exp` `associate-r*`
2×	`flip3--` `sqrt-div` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-l/` `associate-/r/` `-commutative` `associate-/l/`

Counts

4 → 394

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
18.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
147.0ms	(* (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)) x)
11.0ms	(sqrt (- (* z z) (* t a)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* z z) (* t a))
95.0ms	(/ (/ (sqrt (- (* z z) (* t a))) z) y)
154.0ms	(* (/ 1 (/ (/ (sqrt (- (* z z) (* t a))) z) y)) x)
79.0ms	(sqrt (- (* z z) (* t a)))

simplify1.0s

Counts

406 → 406

Iterations

Iter	Nodes
done	5000
1	1825
0	611

prune3.1s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.3b

localize53.0ms

Local error

Found 4 expressions with local error:

4.0b	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`cbrt-prod`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 84

Calls

4 calls:

5.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
8.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
9.0ms	(sqrt (- (* z z) (* t a)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

177.0ms	(cbrt (/ (sqrt (- (* z z) (* t a))) z))
89.0ms	(sqrt (- (* z z) (* t a)))
86.0ms	(sqrt (- (* z z) (* t a)))
84.0ms	(sqrt (- (* z z) (* t a)))

simplify1.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	3717
2	835
1	295
0	147

prune752.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.3b

regimes1.0s

Accuracy

84.3% (3.2b remaining)

Error of 6.6b against oracle of 3.4b and baseline of 23.8b

bsearch89.0ms

Steps

Iters	Range		Point
7	4.962524782877993e+148	5.8027159941114316e+150	7.130903565650381e+148
5	-3.96202307955751e+103	-1.4068852168728814e+103	-3.385971485995103e+103

simplify5.0ms

Iterations

Iter	Nodes
done	37
2	37
1	34
0	27

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.1s	8857×	body	80	valid
214.0ms	2816×	body	80	nan