Details

sample56.0ms

Algorithm

intervals

Results

11.0ms	180×	body	80	valid
9.0ms	29×	body	1280	valid
6.0ms	256×	pre	80	true
6.0ms	24×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	11×	body	160	valid

simplify994.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
2.7b	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
25×	`times-frac`
19×	`distribute-lft-out`
14×	`add-cube-cbrt`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`pow1` `flip3-+` `div-sub` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

2 → 65

Calls

2 calls:

63.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
266.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

series176.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(/ (- beta alpha) (+ (+ alpha beta) 2.0))
98.0ms	(+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts: 71 → 71

prune253.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 16.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
0.0b	(/ alpha (+ (+ alpha beta) 2.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite2.0s

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity`
61×	`add-sqr-sqrt`
56×	`times-frac`
36×	`add-cube-cbrt`
24×	`distribute-lft-out`
13×	`associate-/r` `associate-/l` `distribute-lft-out--`
10×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`add-log-exp`
4×	`pow1` `associate-/r/` `associate-/l/`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`flip3-+` `frac-sub` `flip-+`
1×	`sub-neg` `diff-log` `div-sub`

Counts

4 → 137

Calls

4 calls:

1.6s	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
57.0ms	(/ alpha (+ (+ alpha beta) 2.0))
69.0ms	(/ beta (+ (+ alpha beta) 2.0))
300.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series365.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (- (/ beta (+ (+ alpha beta) 2.0)) (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)) 2.0)
83.0ms	(/ alpha (+ (+ alpha beta) 2.0))
68.0ms	(/ beta (+ (+ alpha beta) 2.0))
112.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify784.0ms

Counts: 149 → 149

prune496.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
0.0b	(/ beta (+ (+ alpha beta) 2.0))
2.7b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
32×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`exp-prod` `distribute-lft-out`
9×	`add-log-exp`
7×	`log-pow`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`pow1` `log-prod` `associate-/r*`
4×	`exp-sum`
3×	`sub-neg` `associate-/l*` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `associate-/r/` `rem-exp-log`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `flip3-+` `div-exp` `rem-log-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 91

Calls

4 calls:

569.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
69.0ms	(/ beta (+ (+ alpha beta) 2.0))
571.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
256.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series430.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0))
78.0ms	(/ beta (+ (+ alpha beta) 2.0))
106.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
126.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify1.7s

Counts: 103 → 103

prune454.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.8b	(cbrt (+ (+ alpha beta) 2.0))
0.8b	(cbrt (+ (+ alpha beta) 2.0))
2.7b	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
2.7b	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

rewrite869.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
7×	`log-pow`
6×	`exp-prod` `distribute-lft-out` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `cbrt-div` `add-cbrt-cube` `difference-of-squares`
2×	`sub-neg` `flip3-+` `times-frac` `pow1/3` `exp-sum` `flip-+` `distribute-lft-out--`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 66

Calls

4 calls:

32.0ms	(cbrt (+ (+ alpha beta) 2.0))
35.0ms	(cbrt (+ (+ alpha beta) 2.0))
513.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
285.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

series507.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (+ (+ alpha beta) 2.0))
152.0ms	(cbrt (+ (+ alpha beta) 2.0))
98.0ms	(log (exp (- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)))
111.0ms	(- (/ alpha (+ (+ alpha beta) 2.0)) 1.0)

simplify958.0ms

Counts: 78 → 78

prune439.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

regimes132.0ms

Accuracy

78% (2.8b remaining)

Error of 5.8b against oracle of 3.0b and baseline of 15.9b

bsearch65.0ms

Steps

Iters	Range		Point
9	32.247679756328765	7389299.1036994485	7316578.694302302

simplify702.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

672.0ms	885×	body	1280	valid
335.0ms	5831×	body	80	valid
220.0ms	740×	body	640	valid
145.0ms	8000×	pre	80	true
81.0ms	362×	body	320	valid
17.0ms	182×	body	160	valid