Details

sample84.0ms

Algorithm

intervals

Results

16.0ms	36×	body	2560	valid
15.0ms	30×	body	1280	valid
14.0ms	187×	body	80	valid
6.0ms	79×	body	80	nan
3.0ms	10×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify143.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	156
6	156
5	152
4	142
3	115
2	64
1	28
0	14

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
7×	`times-frac` `add-cube-cbrt` `associate-/l*`
6×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `flip--`
3×	`distribute-rgt-neg-in` `diff-log`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `div-exp` `associate-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `associate-/r*` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 77

Calls

4 calls:

66.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
6.0ms	(- (* b b) (* 4.0 (* a c)))
26.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
12.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
82.0ms	(- (* b b) (* 4.0 (* a c)))
119.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
90.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify678.0ms

Counts

89 → 89

Iterations

Iter	Nodes
done	5000
2	1618
1	411
0	155

prune535.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* a 2.0) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac`
58×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`associate-/r*`
16×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
13×	`add-cbrt-cube`
12×	`div-exp`
9×	`associate-/r/` `distribute-lft-out`
8×	`distribute-neg-frac` `add-log-exp`
6×	`pow1`
5×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
4×	`neg-mul-1`
3×	`rec-exp` `1-exp` `prod-exp` `sqrt-prod` `associate-/l*`
2×	`flip3--` `sqrt-div` `flip--`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `cbrt-unprod` `pow-flip` `inv-pow`

Counts

4 → 139

Calls

4 calls:

72.0ms	(/ 1 (/ (* a 2.0) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))))
13.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
7.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(/ 1 (/ (* a 2.0) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))))
77.0ms	(- (* b b) (* 4.0 (* a c)))
139.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
112.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.5s

Counts

151 → 151

Iterations

Iter	Nodes
done	5001
2	3039
1	688
0	261

prune640.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (* 2.0 a)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.6b	(- (* b b) (* 4.0 (* a c)))
0.9b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
22.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-sqr-sqrt` `add-cbrt-cube`
12×	`associate-r`
10×	`prod-exp` `add-cube-cbrt`
8×	`add-log-exp`
7×	`pow1` `associate-l`
4×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `div-exp` `cbrt-unprod` `distribute-neg-frac`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+` `distribute-lft-out`
2×	`frac-times` `cbrt-undiv` `rec-exp` `distribute-neg-in` `flip3--` `sqrt-div` `1-exp` `associate-*r/` `flip--`
1×	`distribute-rgt-in` `+-commutative` `rem-sqrt-square` `neg-mul-1` `sum-log` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `-commutative` `distribute-rgt-neg-out` `div-inv` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

140.0ms	(* (/ 1 (* 2.0 a)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
6.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (/ 1 (* 2.0 a)) (- (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
64.0ms	(- (* b b) (* 4.0 (* a c)))
116.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
105.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	3253
1	565
0	184

prune582.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.8b

localize60.0ms

Local error

Found 4 expressions with local error:

0.9b	(+ b (sqrt (- (* b b) (* a (* c 4.0)))))
22.6b	(sqrt (- (* b b) (* a (* c 4.0))))
22.6b	(sqrt (- (* b b) (* a (* c 4.0))))
22.6b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `sqrt-prod`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`add-cbrt-cube` `add-exp-log`
3×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+` `distribute-lft-out`

Counts

4 → 57

Calls

4 calls:

19.0ms	(+ b (sqrt (- (* b b) (* a (* c 4.0)))))
7.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
7.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
13.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series429.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(+ b (sqrt (- (* b b) (* a (* c 4.0)))))
102.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
108.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
103.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify517.0ms

Counts

69 → 69

Iterations

Iter	Nodes
done	5001
2	825
1	197
0	73

prune757.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes433.0ms

Accuracy

85.3% (4.2b remaining)

Error of 10.0b against oracle of 5.8b and baseline of 34.2b

bsearch423.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	7.501979458872916e+77
6	-6.6625002027150184e-136	-1.2670716760605177e-136	-6.596302400897662e-136
9	-1.3974083100475422e-87	-7.780761669250176e-94	-7.877985662156599e-94
10	-4.6999773453873415e+54	-3.4259522644792056e+40	-5.84038254482515e+46

simplify1.3s

Iterations

Iter	Nodes
done	5001
13	2741
12	1453
11	805
10	477
9	309
8	221
7	173
6	141
5	107
4	89
3	85
2	77
1	66
0	46

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.1s	1045×	body	2560	valid
581.0ms	5898×	body	80	valid
397.0ms	875×	body	1280	valid
289.0ms	2811×	body	80	nan
285.0ms	448×	body	640	valid
111.0ms	121×	body	5120	valid
53.0ms	227×	body	320	valid
16.0ms	105×	body	160	valid