Details

sample50.0ms

Algorithm

intervals

Results

10.0ms	35×	body	2560	valid
10.0ms	188×	body	80	valid
7.0ms	28×	body	1280	valid
4.0ms	85×	body	80	nan
3.0ms	14×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	4×	body	160	valid

simplify159.0ms

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

140.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
18.0ms	(- (* b b) (* (* 3 a) c))
23.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series417.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a))
76.0ms	(- (* b b) (* (* 3 a) c))
88.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
111.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1430
1	442
0	170

prune597.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
0.8b	(- (* b b) (* (* 3 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
21.2b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
14×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`fma-def` `add-cube-cbrt` `add-log-exp`
9×	`add-cbrt-cube`
8×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `times-frac` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `sum-log` `flip3--` `sqrt-div` `1-exp` `pow-flip` `flip--` `distribute-lft-out`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `neg-log` `associate-+l-` `cbrt-unprod` `flip-+` `div-inv` `inv-pow`

Counts

4 → 94

Calls

4 calls:

11.0ms	(/ 1 (* 3 a))
9.0ms	(- (* b b) (* (* 3 a) c))
32.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (* 3 a))
81.0ms	(- (* b b) (* (* 3 a) c))
141.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3 a) c))))
106.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5000
3	4257
2	1121
1	380
0	155

prune628.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* -3 a))
1.0b	(fma b b (* c (* -3 a)))
1.6b	(- (sqrt (fma b b (* c (* -3 a)))) b)
21.2b	(sqrt (fma b b (* c (* -3 a))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `associate-r` `*-commutative` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

39.0ms	(* c (* -3 a))
1.0ms	(fma b b (* c (* -3 a)))
24.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
4.0ms	(sqrt (fma b b (* c (* -3 a))))

series340.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* c (* -3 a))
69.0ms	(fma b b (* c (* -3 a)))
121.0ms	(- (sqrt (fma b b (* c (* -3 a)))) b)
116.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify3.0s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	2931
2	835
1	320
0	144

prune543.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.6b

localize75.0ms

Local error

Found 4 expressions with local error:

1.0b	(fma b b (* c (* -3 a)))
4.1b	(* (/ 3 (/ (fma c (* -3 a) 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))) a)
10.6b	(/ (fma c (* -3 a) 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))
21.2b	(sqrt (fma b b (* c (* -3 a))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
84×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
59×	`associate-l`
58×	`add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out`
9×	`associate-/r/`
7×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `cbrt-undiv` `associate-/r*` `flip3-+` `div-exp` `flip-+` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `prod-exp` `sqrt-prod` `cbrt-unprod` `associate-/l*` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `fma-udef`

Counts

4 → 147

Calls

4 calls:

0.0ms	(fma b b (* c (* -3 a)))
89.0ms	(* (/ 3 (/ (fma c (* -3 a) 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))) a)
24.0ms	(/ (fma c (* -3 a) 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))
3.0ms	(sqrt (fma b b (* c (* -3 a))))

series713.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(fma b b (* c (* -3 a)))
253.0ms	(* (/ 3 (/ (fma c (* -3 a) 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))) a)
262.0ms	(/ (fma c (* -3 a) 0) (+ (sqrt (fma b b (* c (* -3 a)))) b))
130.0ms	(sqrt (fma b b (* c (* -3 a))))

simplify2.1s

Counts

159 → 159

Iterations

Iter	Nodes
done	5002
2	2193
1	629
0	261

prune1.1s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.6b

regimes823.0ms

Accuracy

87.4% (3.4b remaining)

Error of 8.7b against oracle of 5.3b and baseline of 32.3b

bsearch226.0ms

Steps

Iters	Range		Point
7	3.170449429657488e+21	2.218413533118306e+23	1.6037393836292316e+23
9	5.111551936031541e-102	3.986693767760393e-93	6.867273651179479e-102
1	-8.312461348155162e+140	-7.521461936906115e+140	-7.644215926145536e+140

simplify21.0ms

Iterations

Iter	Nodes
done	59
1	59
0	47

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.0s	1082×	body	2560	valid
763.0ms	2987×	body	80	nan
643.0ms	5801×	body	80	valid
470.0ms	933×	body	1280	valid
211.0ms	490×	body	640	valid
96.0ms	107×	body	5120	valid
52.0ms	245×	body	320	valid
18.0ms	123×	body	160	valid