Details

sample82.0ms

Algorithm

intervals

Results

18.0ms	155×	body	80	valid
16.0ms	43×	body	2560	valid
8.0ms	26×	body	1280	valid
6.0ms	94×	body	80	nan
5.0ms	19×	body	640	valid
3.0ms	5×	body	5120	valid
2.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	120
5	120
4	112
3	83
2	42
1	22
0	12

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.6b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite91.0ms

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` `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 → 80

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
13.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 3.0 a) c)
66.0ms	(- (* b b) (* (* 3.0 a) c))
129.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
102.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
2	1931
1	360
0	135

prune657.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 13.4b

localize76.0ms

Local error

Found 4 expressions with local error:

16.3b	(cbrt (* (* 3.0 a) c))
16.3b	(cbrt (* (* 3.0 a) c))
16.3b	(cbrt (* (* 3.0 a) c))
21.4b	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite47.0ms

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` `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 → 50

Calls

4 calls:

9.0ms	(cbrt (* (* 3.0 a) c))
9.0ms	(cbrt (* (* 3.0 a) c))
18.0ms	(cbrt (* (* 3.0 a) c))
10.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series622.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(cbrt (* (* 3.0 a) c))
166.0ms	(cbrt (* (* 3.0 a) c))
139.0ms	(cbrt (* (* 3.0 a) c))
180.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify2.7s

Counts

62 → 62

Iterations

Iter	Nodes
done	5000
3	3559
2	672
1	225
0	92

prune541.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 13.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.5b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
21.4b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt c)
30.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
13.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series845.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(cbrt c)
283.0ms	(cbrt c)
152.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))))
138.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1253
1	291
0	112

prune632.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 11.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt (* (cbrt c) (cbrt c)))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))) (cbrt c)))))
21.4b	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))) (cbrt c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt c)
4.0ms	(cbrt (* (cbrt c) (cbrt c)))
18.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))) (cbrt c)))))
9.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))) (cbrt c))))

series908.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt c)
384.0ms	(cbrt (* (cbrt c) (cbrt c)))
155.0ms	(+ (- b) (sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))) (cbrt c)))))
111.0ms	(sqrt (- (* b b) (* (* (* 3.0 a) (* (cbrt c) (* (cbrt (* (cbrt c) (cbrt c))) (cbrt (cbrt c))))) (cbrt c))))

simplify1.5s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1406
1	337
0	133

prune601.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 11.3b

regimes846.0ms

Accuracy

85.4% (3.4b remaining)

Error of 14.8b against oracle of 11.3b and baseline of 34.7b

bsearch190.0ms

Steps

Iters	Range		Point
9	5.75915985305395e-78	3.6929333590207295e-72	3.394285259336288e-72
8	-6.412561728939963e+28	-6.810701174428621e+25	-6.336287344206649e+28

simplify9.0ms

Iterations

Iter	Nodes
done	37
1	37
0	32

end0.0ms

sample3.1s

Algorithm

intervals

Results

609.0ms	1103×	body	2560	valid
536.0ms	5735×	body	80	valid
438.0ms	956×	body	1280	valid
415.0ms	461×	body	640	valid
383.0ms	119×	body	160	valid
222.0ms	2942×	body	80	nan
79.0ms	227×	body	320	valid
56.0ms	106×	body	5120	valid