Details

sample81.0ms

Algorithm

intervals

Results

22.0ms	32×	body	1280	valid
17.0ms	44×	body	2560	valid
10.0ms	167×	body	80	valid
6.0ms	100×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify103.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 4.0 a) c)
0.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite124.0ms

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:

32.0ms	(* (* 4.0 a) c)
51.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(- (* b b) (* (* 4.0 a) c))
22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 4.0 a) c)
125.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms	(- (* b b) (* (* 4.0 a) c))
98.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.9s

Counts

92 → 92

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	135	1109
1	361	1010
2	1922	900
done	5000	893

prune437.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.3b	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
11.3b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite263.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

18.0ms	(- (* b b) (* (* 4.0 a) c))
138.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series753.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b b) (* (* 4.0 a) c))
318.0ms	(/ (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
260.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.5s

Counts

170 → 170

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	263	5076
1	699	4517
2	4581	4197
done	5000	4196

prune782.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.4b

localize51.0ms

Local error

Found 4 expressions with local error:

8.4b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
10.3b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
10×	`fma-neg` `prod-diff`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-prod` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `associate-/r*` `flip--` `log1p-expm1-u`
3×	`associate-/l*`
2×	`neg-mul-1` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 108

Calls

4 calls:

27.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
78.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series576.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
268.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))))))
102.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.5s

Counts

120 → 120

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	189	4229
1	483	2517
2	2724	2380
done	5000	2365

prune667.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.4b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
3.4b	(* (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
11.3b	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
58×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
30×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`sqrt-prod`
8×	`cbrt-undiv` `cbrt-unprod`
7×	`pow1` `distribute-rgt-neg-in` `associate-r` `associate-/r*`
6×	`add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`sqrt-div` `associate-/l/` `unswap-sqr`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 153

Calls

4 calls:

18.0ms	(- (* b b) (* (* 4.0 a) c))
141.0ms	(* (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
109.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (* b b) (* (* 4.0 a) c))
305.0ms	(* (/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))
242.0ms	(/ (+ 0 (* c (* 4.0 a))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
136.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify535.0ms

Counts

165 → 165

Iterations

Useful iterations: done (526.0ms)

Iter	Nodes	Cost
0	268	4670
1	800	4073
done	5000	3633

prune699.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.4b

regimes282.0ms

Accuracy

95.4% (1.0b remaining)

Error of 12.1b against oracle of 11.1b and baseline of 32.3b

bsearch241.0ms

Steps

Iters	Range		Point
8	4.1368702715426593e+145	2.247192940380469e+149	2.1974769882259982e+149
7	1.743450368345407e-128	9.096741835583034e-127	1.769241967981359e-128
4	-5.365119720024443e+91	-2.969789614895389e+91	-3.938820754703496e+91

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	39	85
1	50	85
done	50	85

end0.0ms

sample3.3s

Algorithm

intervals

Results

714.0ms	936×	body	1280	valid
583.0ms	2905×	body	80	nan
579.0ms	1127×	body	2560	valid
550.0ms	5717×	body	80	valid
178.0ms	448×	body	640	valid
123.0ms	223×	body	320	valid
57.0ms	111×	body	5120	valid
14.0ms	112×	body	160	valid