Details

sample347.0ms

Algorithm

intervals

Results

71.0ms	39×	body	1280	valid
61.0ms	20×	body	1280	nan
58.0ms	343×	body	80	nan
26.0ms	154×	body	80	valid
17.0ms	26×	body	640	valid
14.0ms	22×	body	640	nan
12.0ms	24×	body	320	valid
6.0ms	16×	body	320	nan
5.0ms	13×	body	160	valid
1.0ms	3×	body	160	nan

simplify742.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	1370
4	472
3	215
2	101
1	44
0	18

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
0.4b	(* (sqrt 2) t)
13.6b	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
20.5b	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`associate-/r` `times-frac` `associate-l*` `add-log-exp`
4×	`expm1-log1p-u` `sqrt-div` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `-commutative` `div-inv` `associate-/l`

Counts

4 → 94

Calls

4 calls:

64.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
16.0ms	(* (sqrt 2) t)
29.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
81.0ms	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
53.0ms	(* (sqrt 2) t)
268.0ms	(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
1.5s	(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

simplify850.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	2000
2	1605
1	483
0	181

prune676.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.1b

localize40.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
6.5b	(/ (* l l) x)
7.6b	(/ (* 4 (* t t)) x)
27.9b	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `times-frac`
5×	`pow1` `cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `div-inv` `associate-/l*`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 77

Calls

4 calls:

0.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
28.0ms	(/ (* l l) x)
28.0ms	(/ (* 4 (* t t)) x)
1.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x))
21.0ms	(/ (* l l) x)
27.0ms	(/ (* 4 (* t t)) x)
403.0ms	(sqrt (fma 2 (fma t t (/ (* l l) x)) (/ (* 4 (* t t)) x)))

simplify712.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	2030
2	1450
1	393
0	148

prune647.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.0b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) t)
4.0b	(fma (* t t) 2 (* 4 (/ (* t t) x)))
7.6b	(/ (* t t) x)
27.9b	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1` `sqrt-prod`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `times-frac` `associate-r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

7.0ms	(* (sqrt 2) t)
0.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
9.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sqrt 2) t)
77.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
21.0ms	(/ (* t t) x)
467.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

simplify570.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2002
2	930
1	314
0	136

prune618.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
4.0b	(fma (* t t) 2 (* 4 (/ (* t t) x)))
7.6b	(/ (* t t) x)
27.9b	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
17×	`pow1`
15×	`add-cbrt-cube`
9×	`prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt` `pow-prod-down`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `sqrt-prod`
2×	`cbrt-undiv` `div-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `associate-l` `-commutative` `fma-udef` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

64.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
0.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
25.0ms	(/ (* t t) x)
1.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))
71.0ms	(fma (* t t) 2 (* 4 (/ (* t t) x)))
34.0ms	(/ (* t t) x)
483.0ms	(sqrt (fma (/ l (/ x l)) 2 (fma (* t t) 2 (* 4 (/ (* t t) x)))))

simplify642.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	2003
2	1166
1	350
0	141

prune505.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.0b

regimes617.0ms

Accuracy

78.1% (5.1b remaining)

Error of 9.4b against oracle of 4.2b and baseline of 27.8b

bsearch1.3s

Steps

Iters	Range		Point
9	6.304552648946534e+101	1.0488449087684188e+108	9.234874397993673e+103
10	-4.0078265890482388e-174	-2.271177371877917e-185	-5.330429831411802e-184
11	-4.997562010672814e-139	-5.210697667798281e-160	-5.64615525414727e-160
10	-6.1949627884649066e+72	-9.200494817440825e+61	-2.723485209640235e+72

simplify16.0ms

Iterations

Iter	Nodes
done	56
1	56
0	51

end0.0ms

sample9.1s

Algorithm

intervals

Results

2.4s	10352×	body	80	nan
1.5s	5085×	body	80	valid
1.3s	863×	body	1280	valid
889.0ms	1019×	body	640	valid
773.0ms	662×	body	320	valid
643.0ms	607×	body	1280	nan
452.0ms	616×	body	640	nan
288.0ms	345×	body	320	nan
195.0ms	371×	body	160	valid
64.0ms	189×	body	160	nan