Details

sample120.0ms

Algorithm

intervals

Results

26.0ms	19×	body	640	valid
24.0ms	43×	body	2560	valid
16.0ms	155×	body	80	valid
12.0ms	26×	body	1280	valid
8.0ms	94×	body	80	nan
3.0ms	12×	body	320	valid
3.0ms	5×	body	5120	valid
1.0ms	6×	body	160	valid

simplify84.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	128
5	128
4	119
3	86
2	46
1	25
0	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
0.6b	(- (* b b) (* (* 4.0 c) a))
1.5b	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
21.4b	(sqrt (- (* b b) (* (* 4.0 c) a)))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 118

Calls

4 calls:

116.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
13.0ms	(- (* b b) (* (* 4.0 c) a))
84.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
16.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 c) a))) b) a)
58.0ms	(- (* b b) (* (* 4.0 c) a))
101.0ms	(- (sqrt (- (* b b) (* (* 4.0 c) a))) b)
100.0ms	(sqrt (- (* b b) (* (* 4.0 c) a)))

simplify2.5s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	2112
1	509
0	198

prune907.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (* -2.0 (/ c b)) 2.0)
0.0b	(* -2.0 (/ c b))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 60

Calls

2 calls:

10.0ms	(/ (* -2.0 (/ c b)) 2.0)
11.0ms	(* -2.0 (/ c b))

series61.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ (* -2.0 (/ c b)) 2.0)
27.0ms	(* -2.0 (/ c b))

simplify1.1s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
2	1313
1	282
0	110

prune442.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* -2.0 (/ c b)) (* (cbrt 2.0) (cbrt 2.0)))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

25.0ms	(/ (* -2.0 (/ c b)) (* (cbrt 2.0) (cbrt 2.0)))
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)

series216.0ms

Counts

4 → 6

Calls

4 calls:

216.0ms	(/ (* -2.0 (/ c b)) (* (cbrt 2.0) (cbrt 2.0)))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify1.1s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1567
1	247
0	83

prune373.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 5.3b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
1.0b	(cbrt (cbrt 2.0))
1.0b	(cbrt (cbrt 2.0))
1.0b	(cbrt (cbrt 2.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
23×	`pow1`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
12×	`pow1/3`
9×	`associate-r` `add-exp-log` `pow-prod-up`
6×	`pow-plus`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `pow-sqr` `cbrt-unprod` `unswap-sqr`
2×	`pow2`
1×	`associate-l` `pow3` `*-commutative`

Counts

4 → 89

Calls

4 calls:

53.0ms	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
1.0ms	(cbrt (cbrt 2.0))
1.0ms	(cbrt (cbrt 2.0))
6.0ms	(cbrt (cbrt 2.0))

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(* (* (cbrt (cbrt 2.0)) (cbrt (cbrt 2.0))) (cbrt (cbrt 2.0)))
0.0ms	(cbrt (cbrt 2.0))
0.0ms	(cbrt (cbrt 2.0))
0.0ms	(cbrt (cbrt 2.0))

simplify1000.0ms

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
2	608
1	144
0	64

prune514.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.3b

regimes501.0ms

Accuracy

85.5% (4.8b remaining)

Error of 10.4b against oracle of 5.6b and baseline of 39.0b

bsearch206.0ms

Steps

Iters	Range		Point
12	2.4919208328047006e-151	1.0529347607547997e-106	6.484072051994264e-107
8	-6.412561728939963e+28	-6.810701174428621e+25	-6.336287344206649e+28

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	32

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.6s	5735×	body	80	valid
564.0ms	1104×	body	2560	valid
548.0ms	957×	body	1280	valid
212.0ms	2942×	body	80	nan
130.0ms	461×	body	640	valid
77.0ms	226×	body	320	valid
62.0ms	106×	body	5120	valid
57.0ms	119×	body	160	valid