Details

sample66.0ms

Algorithm

intervals

Results

21.0ms	189×	body	80	valid
8.0ms	26×	body	1280	valid
7.0ms	256×	pre	80	true
5.0ms	20×	body	640	valid
3.0ms	15×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
9	4691
8	1531
7	665
6	318
5	164
4	74
3	53
2	34
1	20
0	10

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.6b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

104×	`*-un-lft-identity`
50×	`times-frac`
47×	`add-sqr-sqrt`
34×	`distribute-lft-out`
31×	`fma-def`
25×	`add-cube-cbrt`
11×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-cbrt-cube` `add-exp-log` `associate-/r/` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`expm1-log1p-u` `pow1` `div-sub` `log1p-expm1-u` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `clear-num` `sum-log` `frac-2neg` `flip3--` `div-exp` `associate-+l-` `flip--`

Counts

2 → 100

Calls

2 calls:

59.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
197.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series161.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
76.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5002
2	1431
1	340
0	128

prune460.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.4b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ alpha (+ (+ 2.0 beta) alpha))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.6b	(- (/ alpha (+ (+ 2.0 beta) alpha)) 1.0)

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

182×	`*-un-lft-identity`
91×	`times-frac`
85×	`add-sqr-sqrt`
80×	`add-cube-cbrt`
63×	`prod-diff`
60×	`distribute-lft-out`
21×	`fma-neg`
12×	`associate-/r/`
10×	`associate-/r*`
7×	`add-cbrt-cube` `add-exp-log`
6×	`flip3-+` `flip-+` `div-inv` `associate-/l*`
5×	`add-log-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 179

Calls

3 calls:

58.0ms	(/ alpha (+ (+ 2.0 beta) alpha))
32.0ms	(/ beta (+ (+ alpha beta) 2.0))
265.0ms	(- (/ alpha (+ (+ 2.0 beta) alpha)) 1.0)

series236.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(/ alpha (+ (+ 2.0 beta) alpha))
65.0ms	(/ beta (+ (+ alpha beta) 2.0))
107.0ms	(- (/ alpha (+ (+ 2.0 beta) alpha)) 1.0)

simplify1.4s

Counts

188 → 188

Iterations

Iter	Nodes
done	5000
2	2265
1	573
0	237

prune721.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize43.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (/ alpha (+ (+ 2.0 beta) alpha)) 1.0)
7.7b	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
7.7b	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
7.7b	(cbrt (/ beta (+ 2.0 (+ beta alpha))))

rewrite368.0ms

Algorithm

rewrite-expression-head

Rules

195×	`*-un-lft-identity`
106×	`times-frac`
93×	`add-sqr-sqrt`
88×	`add-cube-cbrt`
63×	`cbrt-prod` `prod-diff` `distribute-lft-out`
21×	`fma-neg`
14×	`associate-/r/`
7×	`flip3-+` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`cbrt-div` `pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 197

Calls

4 calls:

276.0ms	(- (/ alpha (+ (+ 2.0 beta) alpha)) 1.0)
30.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
23.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
20.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))

series759.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (/ alpha (+ (+ 2.0 beta) alpha)) 1.0)
192.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
190.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
270.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))

simplify1.1s

Counts

209 → 209

Iterations

Iter	Nodes
done	5000
2	1898
1	575
0	258

prune967.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize60.0ms

Local error

Found 4 expressions with local error:

7.7b	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
7.7b	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
7.7b	(cbrt (/ beta (+ (+ 2.0 beta) alpha)))
10.1b	(log (exp (cbrt (/ beta (+ (+ 2.0 beta) alpha)))))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
84×	`cbrt-prod`
60×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`distribute-lft-out`
25×	`log-pow`
24×	`exp-prod`
8×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`cbrt-div` `log-prod` `pow1/3`
1×	`rem-log-exp`

Counts

4 → 134

Calls

4 calls:

24.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
21.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
23.0ms	(cbrt (/ beta (+ (+ 2.0 beta) alpha)))
81.0ms	(log (exp (cbrt (/ beta (+ (+ 2.0 beta) alpha)))))

series824.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
214.0ms	(cbrt (/ beta (+ 2.0 (+ beta alpha))))
231.0ms	(cbrt (/ beta (+ (+ 2.0 beta) alpha)))
172.0ms	(log (exp (cbrt (/ beta (+ (+ 2.0 beta) alpha)))))

simplify660.0ms

Counts

146 → 146

Iterations

Iter	Nodes
done	5000
2	1144
1	418
0	230

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

regimes192.0ms

Accuracy

77% (3.1b remaining)

Error of 6.1b against oracle of 3.0b and baseline of 16.5b

bsearch112.0ms

Steps

Iters	Range		Point
8	1.6797771833777472e+17	1.0218839581142054e+21	1.4037838382120008e+19

simplify4.0ms

Iterations

Iter	Nodes
done	46
1	46
0	41

end0.0ms

sample1.8s

Algorithm

intervals

Results

838.0ms	5791×	body	80	valid
246.0ms	880×	body	1280	valid
205.0ms	705×	body	640	valid
152.0ms	8000×	pre	80	true
59.0ms	418×	body	320	valid
20.0ms	206×	body	160	valid