Details

sample94.0ms

Algorithm

intervals

Results

28.0ms	23×	body	1280	valid
22.0ms	192×	body	80	valid
11.0ms	25×	body	640	valid
10.0ms	256×	pre	80	true
3.0ms	10×	body	320	valid
1.0ms	6×	body	160	valid

simplify660.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	2155
3	440
2	95
1	32
0	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.6b

localize36.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

1.6b

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

21.1b

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

rewrite833.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`*-un-lft-identity`
25×	`add-sqr-sqrt` `add-cube-cbrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`associate-/r/`
11×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `associate-/r*` `div-exp` `div-inv`
5×	`add-log-exp`
4×	`frac-times`
3×	`pow1` `flip3--` `insert-posit16` `flip--`
2×	`clear-num` `frac-2neg` `associate-l/` `prod-exp` `associate-r/` `cbrt-unprod`
1×	`+-commutative` `sum-log`

Counts

3 → 114

Calls

3 calls:

164.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

590.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

78.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

series828.0ms

Counts

3 → 9

Calls

3 calls:

311.0ms

(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))

409.0ms

(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

107.0ms

(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i)))

simplify1.0s

Counts

123 → 123

Iterations

Iter	Nodes
2	3003
1	696
0	228

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
2.5b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.8b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite774.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-cbrt-cube` `add-exp-log`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `associate-/r*` `div-exp`
6×	`pow1` `add-log-exp`
4×	`associate-l` `insert-posit16`
3×	`div-sub` `prod-exp` `cbrt-unprod` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `associate-*l/`
1×	`+-commutative` `sum-log` `flip3--` `pow-prod-down` `associate-r/` `-commutative` `flip--`

Counts

4 → 299

Calls

4 calls:

42.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
199.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
397.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
130.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series943.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
240.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
334.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
262.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.2s

Counts

311 → 311

Iterations

Iter	Nodes
2	4548
1	1122
0	385

prune4.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize80.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta)))
2.5b	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
2.8b	(log (exp (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))))
2.8b	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
165×	`add-sqr-sqrt`
158×	`*-un-lft-identity`
114×	`add-cube-cbrt`
69×	`associate-l`
21×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
18×	`add-cbrt-cube` `add-exp-log` `associate-/r/`
12×	`flip3-+` `flip-+`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`log-prod` `associate-r` `log-pow` `insert-posit16`
3×	`exp-prod` `associate-/r*` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `associate-+r+` `distribute-lft-in` `div-sub` `associate-*r/`
1×	`+-commutative` `clear-num` `sum-log` `frac-2neg` `rem-log-exp` `exp-sum` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out` `associate-/l/`

Counts

4 → 236

Calls

4 calls:

217.0ms	(/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta)))
271.0ms	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
29.0ms	(log (exp (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))))
13.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))

series1.0s

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta)))
296.0ms	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
265.0ms	(log (exp (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))))
232.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))

simplify2.7s

Counts

248 → 248

Iterations

Iter	Nodes
2	5126
1	1467
0	403

prune4.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(exp (log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
2.5b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
2.8b	(log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
2.8b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite617.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
134×	`*-un-lft-identity`
99×	`add-sqr-sqrt`
90×	`associate-r`
66×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
8×	`pow1`
6×	`log-prod` `add-log-exp`
5×	`div-inv`
4×	`log-div` `exp-prod` `associate-l` `insert-posit16`
3×	`cbrt-undiv` `div-exp` `exp-sum` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `exp-diff` `associate-*l/` `log-pow`
1×	`+-commutative` `sum-log` `rem-log-exp` `pow-prod-down` `associate-r/` `-commutative` `rem-exp-log`

Counts

4 → 163

Calls

4 calls:

99.0ms	(exp (log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
357.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
63.0ms	(log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
91.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.8s

Counts

4 → 12

Calls

4 calls:

650.0ms	(exp (log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)))
347.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
489.0ms	(log (+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0))
290.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.0s

Counts

175 → 175

Iterations

Iter	Nodes
2	3869
1	929
0	318

prune2.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.7b

regimes410.0ms

Accuracy

13.7% (5.4b remaining)

Error of 11.1b against oracle of 5.7b and baseline of 11.9b

bsearch1.0ms

Steps

Iters	Range		Point
0	9.650645960462008e+196	9.70485616475844e+196	9.677751062610224e+196

simplify10.0ms

Iterations

Iter	Nodes
2	46
1	46
0	38

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	6410×	body	80	valid
455.0ms	491×	body	1280	valid
375.0ms	8000×	pre	80	true
352.0ms	543×	body	640	valid
195.0ms	354×	body	320	valid
57.0ms	202×	body	160	valid