Details

sample189.0ms

Algorithm

intervals

Results

15.0ms	40×	body	2560	valid
12.0ms	35×	body	1280	valid
11.0ms	183×	body	80	valid
6.0ms	79×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	5×	body	160	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	320	valid

simplify47.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	34
5	34
4	32
3	30
2	23
1	15
0	10

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
1.1b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

97.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
39.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
121.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.0s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1655
1	405
0	164

prune618.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.7b

localize34.0ms

Local error

Found 4 expressions with local error:

1.6b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
3.5b	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
7.7b	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
24.2b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
228×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
162×	`add-cube-cbrt`
64×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
45×	`associate-/l*`
33×	`distribute-lft-out`
16×	`neg-mul-1`
15×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/` `distribute-neg-frac`
7×	`flip3-+` `flip-+`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `associate-/l/`
2×	`clear-num` `frac-2neg`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2`

Counts

4 → 289

Calls

4 calls:

9.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
63.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
59.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
3.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
196.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
292.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
114.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify558.0ms

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	1066
0	420

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
1.6b	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
11.6b	(/ (* c a) a)
24.2b	(sqrt (fma a (- c) (pow b_2 2)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

46×	`times-frac`
44×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-lft-out`
8×	`associate-/l*`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod`
2×	`clear-num` `frac-2neg` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `pow1/2` `associate-/l/`

Counts

4 → 115

Calls

4 calls:

26.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
11.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
14.0ms	(/ (* c a) a)
1.0ms	(sqrt (fma a (- c) (pow b_2 2)))

series506.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
110.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
18.0ms	(/ (* c a) a)
116.0ms	(sqrt (fma a (- c) (pow b_2 2)))

simplify1.2s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	2395
1	472
0	185

prune735.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a (- c) (* b_2 b_2))
0.1b	(/ c (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
1.6b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
24.2b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `associate-/l*`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `fma-udef` `div-inv`

Counts

4 → 77

Calls

4 calls:

1.0ms	(fma a (- c) (* b_2 b_2))
16.0ms	(/ c (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
7.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
2.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(fma a (- c) (* b_2 b_2))
295.0ms	(/ c (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))
110.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
107.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify1.7s

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
3	4062
2	761
1	242
0	117

prune569.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes302.0ms

Accuracy

93.5% (1.6b remaining)

Error of 6.9b against oracle of 5.3b and baseline of 29.6b

bsearch225.0ms

Steps

Iters	Range	Point
9	2.1340360609407003e+79	6.102484722804822e+84	2.3453700250865973e+84
6	-9.106238092000907e-243	-2.101224228167501e-243	-2.1209008810311313e-243
8	-7.706925888451307e+24	-4.0529501114613944e+21	-7.604193036648139e+24

Iters

Range

Point

2.1340360609407003e+79

6.102484722804822e+84

2.3453700250865973e+84

-9.106238092000907e-243

-2.101224228167501e-243

-2.1209008810311313e-243

-7.706925888451307e+24

-4.0529501114613944e+21

-7.604193036648139e+24

simplify10.0ms

Iterations

Iter	Nodes
done	53
3	53
2	50
1	42
0	34

end0.0ms

sample2.8s

Algorithm

intervals

Results

818.0ms	1095×	body	2560	valid
494.0ms	5778×	body	80	valid
383.0ms	933×	body	1280	valid
336.0ms	2882×	body	80	nan
152.0ms	446×	body	640	valid
84.0ms	229×	body	320	valid
41.0ms	93×	body	5120	valid
14.0ms	123×	body	160	valid