Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	191×	body	80	valid
8.0ms	36×	body	2560	valid
3.0ms	20×	body	1280	valid
3.0ms	77×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid

simplify11.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9
done	118	9

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
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×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
9.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* 3.0 a) c)
50.0ms	(- (* b b) (* (* 3.0 a) c))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
76.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467
done	5002	467

prune243.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize13.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

21.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
81.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify110.0ms

Counts

100 → 100

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	234	668
1	888	610
2	3709	588
3	5001	584
done	5001	584

prune401.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt b)
1.0b	(- (* b b) (* (* 3.0 a) c))
21.6b	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `pow1/3` `diff-log` `prod-diff` `fma-udef`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt b)
8.0ms	(- (* b b) (* (* 3.0 a) c))
0.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
11.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt b)
49.0ms	(- (* b b) (* (* 3.0 a) c))
140.0ms	(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (sqrt (- (* b b) (* (* 3.0 a) c))))
74.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify108.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	244	479
1	840	434
2	3607	420
3	5001	419
done	5001	419

prune238.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.3b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
1.5b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.3b	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
24.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
22.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
20.0ms	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 3.0 a) c))
84.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
83.0ms	(exp (log (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify131.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	303	704
1	1127	634
2	4782	595
3	5001	595
done	5001	595

prune271.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 11.1b

regimes361.0ms

Accuracy

97% (0.6b remaining)

Error of 12.2b against oracle of 11.6b and baseline of 33.3b

bsearch176.0ms

Steps

Iters	Range	Point
10	3.439700743057548e+134	6.291895909276075e+152	8.327899021808038e+148
10	9.086592929781624e-148	1.9902982141109294e-134	1.2061568841925156e-138
6	-4.2638646006519825e+105	-4.3760586339396263e+104	-3.248710458425433e+105

Iters

Range

Point

3.439700743057548e+134

6.291895909276075e+152

8.327899021808038e+148

9.086592929781624e-148

1.9902982141109294e-134

1.2061568841925156e-138

-4.2638646006519825e+105

-4.3760586339396263e+104

-3.248710458425433e+105

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	37
1	52	37
2	52	37
done	52	37

end0.0ms

sample1.2s

Algorithm

intervals

Results

236.0ms	1117×	body	2560	valid
210.0ms	5758×	body	80	valid
158.0ms	904×	body	1280	valid
94.0ms	2850×	body	80	nan
62.0ms	474×	body	640	valid
37.0ms	129×	body	5120	valid
21.0ms	216×	body	320	valid
9.0ms	107×	body	160	valid