Details

sample158.0ms

Algorithm

intervals

Results

10.0ms	186×	body	80	valid
9.0ms	30×	body	2560	valid
7.0ms	102×	body	80	nan
5.0ms	23×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite124.0ms

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:

68.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
17.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
41.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

112 → 112

Iterations

Iter	Nodes
done	5001
2	1655
1	405
0	164

prune781.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
3.4b	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
10.8b	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
22.9b	(sqrt (fma a (- c) (* b_2 b_2)))

rewrite114.0ms

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:

6.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
51.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
42.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
1.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

series715.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))
225.0ms	(/ (/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2)))))) a)
215.0ms	(/ (+ 0 (* a c)) (- (+ b_2 (sqrt (fma a (- c) (* b_2 b_2))))))
134.0ms	(sqrt (fma a (- c) (* b_2 b_2)))

simplify653.0ms

Counts

301 → 301

Iterations

Iter	Nodes
done	5000
1	1066
0	420

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize60.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
1.8b	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
22.9b	(sqrt (fma a (- c) (pow b_2 2)))
22.9b	(sqrt (fma a (- c) (pow b_2 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `fma-def` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

11.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
11.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
2.0ms	(sqrt (fma a (- c) (pow b_2 2)))
2.0ms	(sqrt (fma a (- c) (pow b_2 2)))

series452.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
113.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
121.0ms	(sqrt (fma a (- c) (pow b_2 2)))
108.0ms	(sqrt (fma a (- c) (pow b_2 2)))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5000
3	2401
2	447
1	136
0	59

prune856.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
1.8b	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
15.8b	(/ (* c a) a)
22.9b	(sqrt (fma a (- c) (pow b_2 2)))

rewrite71.0ms

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:

34.0ms	(/ (/ (* 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))))
18.0ms	(/ (* c a) a)
2.0ms	(sqrt (fma a (- c) (pow b_2 2)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(/ (/ (* c a) a) (+ b_2 (sqrt (fma a (- c) (pow b_2 2)))))
92.0ms	(+ b_2 (sqrt (fma a (- c) (pow b_2 2))))
8.0ms	(/ (* c a) a)
112.0ms	(sqrt (fma a (- c) (pow b_2 2)))

simplify1.3s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
2	2395
1	472
0	185

prune791.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.4b

regimes387.0ms

Accuracy

89.9% (2.6b remaining)

Error of 8.1b against oracle of 5.4b and baseline of 31.6b

bsearch286.0ms

Steps

Iters	Range		Point
9	6.258218916731328e+93	1.8883840965187804e+99	2.284582175117603e+94
10	1.0098271411010356e-246	1.1833165058303425e-229	5.436810835085153e-239
9	-3.792961868720521e+75	-7.261872368850313e+67	-3.5695008721667037e+75

simplify10.0ms

Iterations

Iter	Nodes
done	51
1	51
0	44

end0.0ms

sample3.1s

Algorithm

intervals

Results

931.0ms	5961×	body	80	valid
509.0ms	1055×	body	2560	valid
419.0ms	880×	body	1280	valid
250.0ms	2944×	body	80	nan
205.0ms	451×	body	640	valid
59.0ms	109×	body	160	valid
49.0ms	97×	body	5120	valid
41.0ms	218×	body	320	valid