Details

sample98.0ms

Algorithm

intervals

Results

31.0ms	28×	body	1280	valid
16.0ms	184×	body	80	valid
13.0ms	25×	body	2560	valid
8.0ms	22×	body	640	valid
6.0ms	69×	body	80	nan
3.0ms	4×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify172.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	140
5	135
4	130
3	110
2	63
1	29
0	14

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
0.9b	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
1.0b	(- (* b b) (* 4 (* a c)))
19.8b	(sqrt (- (* b b) (* 4 (* a c))))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt` `prod-diff`
60×	`*-un-lft-identity`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

87.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
34.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
16.0ms	(- (* b b) (* 4 (* a c)))
16.0ms	(sqrt (- (* b b) (* 4 (* a c))))

series407.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))
119.0ms	(- (- b) (sqrt (- (* b b) (* 4 (* a c)))))
58.0ms	(- (* b b) (* 4 (* a c)))
116.0ms	(sqrt (- (* b b) (* 4 (* a c))))

simplify1.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	1808
1	595
0	239

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (* 2 a))
0.9b	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
1.0b	(fma -4 (* a c) (* b b))
19.8b	(sqrt (fma -4 (* a c) (* b b)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `prod-diff`
48×	`add-cube-cbrt`
36×	`sqrt-prod`
24×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
10×	`fma-neg`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`neg-mul-1` `times-frac` `associate-/l*`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `fma-udef` `div-inv`

Counts

4 → 153

Calls

4 calls:

33.0ms	(/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (* 2 a))
25.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
0.0ms	(fma -4 (* a c) (* b b))
2.0ms	(sqrt (fma -4 (* a c) (* b b)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ (- (- b) (sqrt (fma -4 (* a c) (* b b)))) (* 2 a))
114.0ms	(- (- b) (sqrt (fma -4 (* a c) (* b b))))
97.0ms	(fma -4 (* a c) (* b b))
104.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify1.6s

Counts

165 → 165

Iterations

Iter	Nodes
done	5003
2	1394
1	499
0	213

prune950.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* a c) (* b b))
19.8b	(sqrt (fma -4 (* a c) (* b b)))
19.8b	(sqrt (fma -4 (* a c) (* b b)))
19.8b	(sqrt (fma -4 (* a c) (* b b)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma -4 (* a c) (* b b))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(fma -4 (* a c) (* b b))
133.0ms	(sqrt (fma -4 (* a c) (* b b)))
96.0ms	(sqrt (fma -4 (* a c) (* b b)))
113.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.3s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
4	2142
3	474
2	126
1	61
0	40

prune519.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

localize55.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma -4 (* a c) (* b b))
10.9b	(- (- b) (* (sqrt (sqrt (fma -4 (* a c) (* b b)))) (sqrt (sqrt (fma -4 (* a c) (* b b))))))
19.8b	(sqrt (fma -4 (* a c) (* b b)))
19.8b	(sqrt (fma -4 (* a c) (* b b)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`rem-sqrt-square` `neg-mul-1` `sqrt-pow1` `pow1/2` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `fma-udef` `flip--` `difference-of-squares`

Counts

4 → 81

Calls

4 calls:

0.0ms	(fma -4 (* a c) (* b b))
13.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* a c) (* b b)))) (sqrt (sqrt (fma -4 (* a c) (* b b))))))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))
1.0ms	(sqrt (fma -4 (* a c) (* b b)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(fma -4 (* a c) (* b b))
130.0ms	(- (- b) (* (sqrt (sqrt (fma -4 (* a c) (* b b)))) (sqrt (sqrt (fma -4 (* a c) (* b b))))))
112.0ms	(sqrt (fma -4 (* a c) (* b b)))
120.0ms	(sqrt (fma -4 (* a c) (* b b)))

simplify2.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	1888
2	583
1	230
0	107

prune549.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.1b

regimes387.0ms

Accuracy

83.1% (4.7b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 33.6b

bsearch187.0ms

Steps

Iters	Range		Point
9	1.2511213927906696e+122	3.1675615346558484e+127	2.927598127340643e+124
10	-2.8993282234165347e-22	-3.09682517328325e-32	-3.136683434005781e-32

simplify7.0ms

Iterations

Iter	Nodes
done	27
1	27
0	23

end0.0ms

sample3.2s

Algorithm

intervals

Results

915.0ms	5780×	body	80	valid
721.0ms	923×	body	1280	valid
650.0ms	1096×	body	2560	valid
282.0ms	2933×	body	80	nan
168.0ms	472×	body	640	valid
82.0ms	228×	body	320	valid
53.0ms	98×	body	5120	valid
16.0ms	114×	body	160	valid