Details

sample104.0ms

Algorithm

intervals

Results

20.0ms	28×	body	1280	valid
17.0ms	35×	body	2560	valid
15.0ms	188×	body	80	valid
7.0ms	85×	body	80	nan
5.0ms	14×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify367.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	75
2	40
1	22
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.8b	(- (* b b) (* (* 3.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

141.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms	(- (* b b) (* (* 3.0 a) c))
36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series602.0ms

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
87.0ms	(- (* b b) (* (* 3.0 a) c))
158.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
141.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify3.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5004
2	1415
1	442
0	171

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize86.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* a (* 3.0 c))))) (* 3.0 a))
0.8b	(- (* b b) (* a (* 3.0 c)))
1.6b	(+ (- b) (sqrt (- (* b b) (* a (* 3.0 c)))))
21.2b	(sqrt (- (* b b) (* a (* 3.0 c))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 94

Calls

4 calls:

116.0ms	(/ (+ (- b) (sqrt (- (* b b) (* a (* 3.0 c))))) (* 3.0 a))
24.0ms	(- (* b b) (* a (* 3.0 c)))
42.0ms	(+ (- b) (sqrt (- (* b b) (* a (* 3.0 c)))))
30.0ms	(sqrt (- (* b b) (* a (* 3.0 c))))

series707.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(/ (+ (- b) (sqrt (- (* b b) (* a (* 3.0 c))))) (* 3.0 a))
113.0ms	(- (* b b) (* a (* 3.0 c)))
179.0ms	(+ (- b) (sqrt (- (* b b) (* a (* 3.0 c)))))
160.0ms	(sqrt (- (* b b) (* a (* 3.0 c))))

simplify3.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1411
1	449
0	172

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.8b	(- (* b b) (* (* 3.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `pow1` `fma-def` `add-log-exp`
9×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`sum-log` `flip3--` `sqrt-div` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `associate-+l-` `flip-+`

Counts

4 → 84

Calls

4 calls:

33.0ms	(* (* 3.0 a) c)
23.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
29.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series442.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* 3.0 a) c)
93.0ms	(- (* b b) (* (* 3.0 a) c))
179.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
119.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify7.8s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
3	4057
2	1072
1	354
0	139

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize81.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* c a) 3.0)
0.8b	(- (* b b) (* (* c a) 3.0))
1.6b	(- (sqrt (- (* b b) (* (* c a) 3.0))) b)
21.2b	(sqrt (- (* b b) (* (* c a) 3.0)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 98

Calls

4 calls:

33.0ms	(* (* c a) 3.0)
11.0ms	(- (* b b) (* (* c a) 3.0))
90.0ms	(- (sqrt (- (* b b) (* (* c a) 3.0))) b)
23.0ms	(sqrt (- (* b b) (* (* c a) 3.0)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* c a) 3.0)
77.0ms	(- (* b b) (* (* c a) 3.0))
153.0ms	(- (sqrt (- (* b b) (* (* c a) 3.0))) b)
143.0ms	(sqrt (- (* b b) (* (* c a) 3.0)))

simplify7.7s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
3	4307
2	1116
1	412
0	166

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

regimes1.9s

Accuracy

89.2% (3.2b remaining)

Error of 8.6b against oracle of 5.4b and baseline of 34.7b

bsearch307.0ms

Steps

Iters	Range		Point
7	3.170449429657488e+21	2.218413533118306e+23	6.70315309832186e+21
10	6.5910522195145e-211	2.211124378328604e-200	3.371096935837412e-203
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-1.2705286994550075e+152

simplify18.0ms

Iterations

Iter	Nodes
done	48
1	48
0	41

end0.0ms

sample3.4s

Algorithm

intervals

Results

886.0ms	5801×	body	80	valid
616.0ms	1082×	body	2560	valid
440.0ms	107×	body	5120	valid
362.0ms	933×	body	1280	valid
314.0ms	2987×	body	80	nan
160.0ms	490×	body	640	valid
52.0ms	245×	body	320	valid
19.0ms	123×	body	160	valid