Details

sample106.0ms

Algorithm

intervals

Results

26.0ms	199×	body	80	valid
21.0ms	9×	body	160	valid
13.0ms	19×	body	1280	valid
12.0ms	256×	pre	80	true
12.0ms	21×	body	640	valid
3.0ms	8×	body	320	valid

simplify659.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize55.0ms

Local error

Found 3 expressions with local error:

0.1b

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

2.6b

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

18.8b

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

rewrite772.0ms

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))

529.0ms

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

75.0ms

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

series850.0ms

Counts

3 → 9

Calls

3 calls:

364.0ms

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

371.0ms

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

116.0ms

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

simplify1.1s

Counts

123 → 123

Iterations

Iter	Nodes
2	3003
1	696
0	228

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
1.1b	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
5.3b	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite634.0ms

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:

59.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
153.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
303.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
107.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series1.1s

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2 i)))
260.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
340.0ms	(* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)))
309.0ms	(+ (* (+ beta alpha) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.4s

Counts

311 → 311

Iterations

Iter	Nodes
2	4548
1	1122
0	385

prune2.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta)))
1.1b	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
5.3b	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))
5.3b	(log (exp (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))))

rewrite454.0ms

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:

191.0ms	(/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta)))
232.0ms	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
7.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))
16.0ms	(log (exp (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))))

series977.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta)))
305.0ms	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
217.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))
242.0ms	(log (exp (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))))

simplify2.4s

Counts

248 → 248

Iterations

Iter	Nodes
2	5090
1	1468
0	403

prune3.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.8b

localize65.0ms

Local error

Found 4 expressions with local error:

1.1b	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
4.4b	(log (exp (sqrt (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))))))
5.3b	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))
5.3b	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

111×	`times-frac`
84×	`add-sqr-sqrt`
77×	`*-un-lft-identity`
69×	`associate-l`
57×	`add-cube-cbrt`
13×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`flip3-+` `associate-/r/` `flip-+` `add-log-exp`
7×	`pow1` `log-pow`
6×	`exp-prod`
4×	`associate-+r+` `associate-r` `insert-posit16` `div-inv`
3×	`distribute-rgt-in` `cbrt-undiv` `log-prod` `distribute-lft-in` `div-exp` `prod-exp` `sqrt-prod` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `+-commutative` `sum-log` `associate-*r/`
1×	`rem-log-exp` `pow-prod-down` `associate-l/` `-commutative` `distribute-lft-out`

Counts

4 → 146

Calls

4 calls:

282.0ms	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
12.0ms	(log (exp (sqrt (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))))))
6.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))
9.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))

series2.2s

Counts

4 → 12

Calls

4 calls:

279.0ms	(* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))
1.3s	(log (exp (sqrt (+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta))))))
258.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))
281.0ms	(+ 1.0 (* (/ (/ (- beta alpha) (+ (+ 2.0 (+ alpha beta)) (* 2 i))) (+ (* 2 i) (+ alpha beta))) (+ alpha beta)))

simplify1.6s

Counts

158 → 158

Iterations

Iter	Nodes
2	4089
1	1232
0	321

prune2.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

regimes487.0ms

Accuracy

14.3% (5.7b remaining)

Error of 11.6b against oracle of 5.9b and baseline of 12.5b

bsearch131.0ms

Steps

Iters	Range		Point
7	2.1027794302435606e+105	3.5400380850047944e+106	3.158427829609547e+106

simplify14.0ms

Iterations

Iter	Nodes
2	40
1	40
0	33

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	6351×	body	80	valid
851.0ms	8000×	pre	80	true
514.0ms	520×	body	1280	valid
391.0ms	568×	body	640	valid
225.0ms	347×	body	320	valid
67.0ms	214×	body	160	valid