Details

sample88.0ms

Algorithm

intervals

Results

20.0ms	33×	body	2560	valid
19.0ms	185×	body	80	valid
15.0ms	32×	body	1280	valid
8.0ms	97×	body	80	nan
4.0ms	12×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	4×	body	160	valid

simplify98.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 33.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* 3 a) c)
0.6b	(- (* b b) (* (* 3 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite51.0ms

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:

17.0ms	(* (* 3 a) c)
8.0ms	(- (* b b) (* (* 3 a) c))
14.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* 3 a) c)
52.0ms	(- (* b b) (* (* 3 a) c))
97.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
109.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	2000
3	2000
2	1086
1	352
0	138

prune560.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.3b

localize47.0ms

Local error

Found 4 expressions with local error:

13.2b	(cbrt (* (* 3 a) c))
13.2b	(cbrt (* (* 3 a) c))
13.2b	(cbrt (* (* 3 a) c))
22.2b	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`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×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`

Counts

4 → 54

Calls

4 calls:

9.0ms	(cbrt (* (* 3 a) c))
9.0ms	(cbrt (* (* 3 a) c))
16.0ms	(cbrt (* (* 3 a) c))
19.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

series610.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(cbrt (* (* 3 a) c))
138.0ms	(cbrt (* (* 3 a) c))
137.0ms	(cbrt (* (* 3 a) c))
187.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3 a) c)) (cbrt (* (* 3 a) c))) (cbrt (* (* 3 a) c)))))

simplify1.3s

Counts

66 → 66

Iterations

Iter	Nodes
done	2060
4	2060
3	1778
2	527
1	217
0	93

prune436.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3 a) c))
13.3b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))
22.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3 a) c))
9.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
24.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* b b) (* (* 3 a) c))
142.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3 a) c))))))
120.0ms	(sqrt (- (* b b) (* (* 3 a) c)))
117.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify987.0ms

Counts

91 → 91

Iterations

Iter	Nodes
done	2003
3	2003
2	886
1	282
0	109

prune608.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

localize67.0ms

Local error

Found 4 expressions with local error:

10.2b	(+ (- b) (* (sqrt (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3 a) c))))))
22.9b	(cbrt (- (* b b) (* (* 3 a) c)))
22.9b	(cbrt (- (* b b) (* (* 3 a) c)))
22.9b	(cbrt (- (* b b) (* (* 3 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `fma-def` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod`
8×	`add-log-exp`
6×	`cbrt-div`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `flip3--` `pow1/3` `flip--`
2×	`sum-log`
1×	`neg-sub0` `+-commutative` `neg-mul-1` `flip3-+` `neg-log` `associate-+l-` `flip-+`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+ (- b) (* (sqrt (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3 a) c))))))
5.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
5.0ms	(cbrt (- (* b b) (* (* 3 a) c)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (- b) (* (sqrt (* (cbrt (- (* b b) (* (* 3 a) c))) (cbrt (- (* b b) (* (* 3 a) c))))) (sqrt (cbrt (- (* b b) (* (* 3 a) c))))))
168.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
128.0ms	(cbrt (- (* b b) (* (* 3 a) c)))
127.0ms	(cbrt (- (* b b) (* (* 3 a) c)))

simplify1.0s

Counts

86 → 86

Iterations

Iter	Nodes
done	2001
3	2001
2	952
1	294
0	110

prune575.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.3b

regimes581.0ms

Accuracy

84.4% (3.3b remaining)

Error of 15.5b against oracle of 12.2b and baseline of 33.1b

bsearch168.0ms

Steps

Iters	Range		Point
7	2.6599168228204088e-39	1.6102415927742825e-37	5.700960046364564e-39
9	-2.3702445877051193e+75	-7.530140089969592e+69	-4.179536313363076e+72

simplify5.0ms

Iterations

Iter	Nodes
done	35
1	35
0	31

end0.0ms

sample4.3s

Algorithm

intervals

Results

971.0ms	1105×	body	2560	valid
914.0ms	5935×	body	80	valid
862.0ms	2940×	body	80	nan
601.0ms	843×	body	1280	valid
272.0ms	437×	body	640	valid
171.0ms	120×	body	5120	valid
84.0ms	210×	body	320	valid
53.0ms	111×	body	160	valid