Details

sample80.0ms

Algorithm

intervals

Results

25.0ms	204×	body	80	valid
13.0ms	18×	body	640	valid
10.0ms	256×	pre	80	true
10.0ms	17×	body	1280	valid
4.0ms	12×	body	320	valid
1.0ms	5×	body	160	valid

simplify498.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.4b

localize36.0ms

Local error

Found 3 expressions with local error:

0.1b

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

2.0b

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

19.2b

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

rewrite669.0ms

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:

162.0ms

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

455.0ms

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

48.0ms

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

series941.0ms

Counts

3 → 9

Calls

3 calls:

378.0ms

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

435.0ms

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

128.0ms

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

simplify964.0ms

Counts

123 → 123

Iterations

Iter	Nodes
2	2969
1	697
0	228

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.9b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite980.0ms

Algorithm

rewrite-expression-head

Rules

1250×	`times-frac`
1055×	`*-un-lft-identity`
619×	`add-sqr-sqrt`
461×	`add-cube-cbrt`
218×	`distribute-lft-out`
96×	`associate-/l*`
79×	`distribute-lft-out--` `difference-of-squares`
60×	`associate-/r/`
33×	`div-inv`
30×	`associate-/r*`
26×	`flip3--` `flip--`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`associate-/l/`
4×	`pow1` `flip3-+` `flip-+` `insert-posit16`
3×	`clear-num` `frac-2neg`
1×	`+-commutative` `sum-log`

Counts

4 → 649

Calls

4 calls:

65.0ms	(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
202.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
65.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
610.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series1.4s

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))
314.0ms	(/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
116.0ms	(/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)))
803.0ms	(+ (/ (/ (+ alpha beta) (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

simplify2.7s

Counts

661 → 661

Iterations

Iter	Nodes
2	5800
1	1894
0	709

prune8.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.8b

localize94.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) (* 2 i)))
0.8b	(cbrt (+ (+ alpha beta) (* 2 i)))
0.8b	(cbrt (+ (+ alpha beta) (* 2 i)))
3.0b	(+ (* (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) 1) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (+ (+ alpha beta) (* 2 i))) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16`
3×	`pow1/3`
1×	`+-commutative` `sum-log`

Counts

4 → 54

Calls

4 calls:

20.0ms	(cbrt (+ (+ alpha beta) (* 2 i)))
16.0ms	(cbrt (+ (+ alpha beta) (* 2 i)))
12.0ms	(cbrt (+ (+ alpha beta) (* 2 i)))
253.0ms	(+ (* (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) 1) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (+ (+ alpha beta) (* 2 i))) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

series999.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt (+ (+ alpha beta) (* 2 i)))
205.0ms	(cbrt (+ (+ alpha beta) (* 2 i)))
257.0ms	(cbrt (+ (+ alpha beta) (* 2 i)))
369.0ms	(+ (* (/ (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (/ (* (cbrt (+ (+ alpha beta) (* 2 i))) (cbrt (+ (+ alpha beta) (* 2 i)))) 1)) 1) (/ (/ (cbrt (+ alpha beta)) (/ (cbrt (+ (+ alpha beta) (* 2 i))) (- beta alpha))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))) 1.0)

simplify2.6s

Counts

66 → 66

Iterations

Iter	Nodes
3	4417
2	952
1	318
0	118

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
0.1b	(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
0.4b	(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
3.7b	(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

5615×	`times-frac`
3877×	`*-un-lft-identity`
2481×	`add-sqr-sqrt`
1995×	`add-cube-cbrt`
698×	`distribute-lft-out`
299×	`associate-/l*`
243×	`distribute-lft-out--` `difference-of-squares`
210×	`associate-/r/`
108×	`div-inv`
98×	`associate-/r*`
81×	`flip3--` `flip--`
62×	`add-exp-log`
43×	`div-exp`
32×	`add-cbrt-cube`
22×	`flip3-+` `flip-+`
19×	`cbrt-undiv`
6×	`rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
4×	`insert-posit16`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`+-commutative` `sum-log` `pow-flip` `inv-pow`

Counts

4 → 1936

Calls

4 calls:

95.0ms	(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
191.0ms	(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
43.0ms	(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
604.0ms	(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

181.0ms	(/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))
329.0ms	(/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0))
144.0ms	(/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta)))
376.0ms	(+ (/ (/ 1 (/ (/ (+ (+ alpha beta) (* 2 i)) (- beta alpha)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0)

simplify10.4s

Counts

1948 → 1948

Iterations

Iter	Nodes
1	5024
0	1903

prune28.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.8b

regimes303.0ms

Accuracy

0% (6.6b remaining)

Error of 12.4b against oracle of 5.8b and baseline of 12.4b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	32
1	32
0	25

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.2s	6350×	body	80	valid
580.0ms	550×	body	1280	valid
431.0ms	552×	body	640	valid
386.0ms	8000×	pre	80	true
158.0ms	354×	body	320	valid
61.0ms	194×	body	160	valid