Details

sample33.0ms

Algorithm

intervals

Results

7.0ms	193×	body	80	valid
4.0ms	20×	body	1280	valid
4.0ms	256×	pre	80	true
3.0ms	22×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	9×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	102	29
3	452	29
4	2090	29
done	5001	29

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b

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

2.1b

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

22.7b

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

rewrite785.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 111

Calls

3 calls:

177.0ms

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

553.0ms

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

51.0ms

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

series629.0ms

Counts

3 → 9

Calls

3 calls:

252.0ms

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

292.0ms

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

85.0ms

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

simplify1.1s

Counts

120 → 120

Iterations

Useful iterations: 2 (394.0ms)

Iter	Nodes	Cost
0	225	4035
1	675	3821
2	2949	3577
done	5000	3577

prune347.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite698.0ms

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-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

44.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
178.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
361.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
98.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
370.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
247.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
306.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify1.8s

Counts

307 → 307

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	385	9712
1	1051	9275
2	4616	8911
done	5002	8909

prune787.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.3b

localize17.0ms

Local error

Found 4 expressions with local error:

2.5b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.5b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
2.5b	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
4.1b	(+ (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))) 1.0)

rewrite314.0ms

Algorithm

rewrite-expression-head

Rules

63×	`cbrt-prod`
49×	`add-sqr-sqrt` `*-un-lft-identity`
45×	`times-frac`
31×	`add-cube-cbrt`
9×	`distribute-lft-out--` `difference-of-squares`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
3×	`cbrt-div` `pow1/3` `div-inv`
1×	`+-commutative` `sum-log`

Counts

4 → 101

Calls

4 calls:

20.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
21.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
21.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
248.0ms	(+ (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))) 1.0)

series1.5s

Counts

4 → 12

Calls

4 calls:

388.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
385.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
395.0ms	(cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
343.0ms	(+ (* (+ alpha beta) (/ (* (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (cbrt (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))))) 1.0)

simplify1.8s

Counts

113 → 113

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	153	3275
1	351	3218
2	979	2634
3	3750	2550
done	5001	2538

prune442.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
2.1b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
4.1b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite870.0ms

Algorithm

rewrite-expression-head

Rules

306×	`times-frac`
275×	`*-un-lft-identity`
196×	`add-sqr-sqrt`
133×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
27×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
21×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`cbrt-prod`
11×	`div-inv`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`associate-l` `associate-/r*`
3×	`unpow-prod-down` `cube-prod` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-div` `frac-times` `cbrt-div` `div-sub` `associate-*l/`
1×	`+-commutative` `cube-mult` `frac-2neg` `pow1/3` `unpow3` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `rem-cbrt-cube` `associate-/l/` `sqr-pow`

Counts

4 → 278

Calls

4 calls:

188.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
196.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
365.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
100.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
299.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
249.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
309.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify2.1s

Counts

290 → 290

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	404	10304
1	1093	9687
2	4775	9218
done	5002	9216

prune855.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.3b

regimes307.0ms

Accuracy

77.4% (1.6b remaining)

Error of 7.3b against oracle of 5.7b and baseline of 12.6b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	78
1	43	78
done	43	78

end0.0ms

sample833.0ms

Algorithm

intervals

Results

230.0ms	6316×	body	80	valid
121.0ms	8000×	pre	80	true
100.0ms	538×	body	1280	valid
88.0ms	590×	body	640	valid
39.0ms	365×	body	320	valid
14.0ms	191×	body	160	valid