Details

sample223.0ms

Algorithm

intervals

Results

82.0ms	87×	body	2560	valid
57.0ms	60×	body	10240	exit
46.0ms	90×	body	1280	valid
11.0ms	41×	body	640	valid
6.0ms	316×	pre	80	true
3.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	15×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	239	24
4	653	24
5	2845	24
done	5001	24

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.2b	(- (exp (* b eps)) 1.0)
3.9b	(- (exp (* a eps)) 1.0)
5.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt` `flip3--` `*-un-lft-identity` `flip--` `add-log-exp`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `frac-times` `add-cube-cbrt` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 73

Calls

4 calls:

21.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
4.0ms	(- (exp (* b eps)) 1.0)
4.0ms	(- (exp (* a eps)) 1.0)
4.0ms	(- (exp (* (+ a b) eps)) 1.0)

series450.0ms

Counts

4 → 12

Calls

4 calls:

334.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
31.0ms	(- (exp (* b eps)) 1.0)
38.0ms	(- (exp (* a eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify752.0ms

Counts

85 → 85

Iterations

Useful iterations: 2 (177.0ms)

Iter	Nodes	Cost
0	174	1783
1	484	1741
2	2066	1427
done	5000	1427

prune314.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 b) (/ 1 a))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

18.0ms

(+ (/ 1 b) (/ 1 a))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(+ (/ 1 b) (/ 1 a))

simplify2.0s

Counts

22 → 22

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	40	229
1	102	216
2	222	210
3	491	194
4	942	194
5	2258	194
done	5000	194

prune49.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-r/` `associate-l/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

118.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
16.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series349.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
83.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
79.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
86.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify1.5s

Counts

171 → 171

Iterations

Useful iterations: 3 (812.0ms)

Iter	Nodes	Cost
0	178	3472
1	391	3024
2	994	2871
3	3458	2483
done	5001	2483

prune339.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.6b	(cbrt (+ (/ 1 b) (/ 1 a)))
0.9b	(pow (cbrt (cbrt (+ (/ 1 b) (/ 1 a)))) 4)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

59×	`*-un-lft-identity`
53×	`cbrt-prod`
28×	`distribute-lft-out`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`unpow-prod-down` `div-inv`
9×	`cbrt-div`
5×	`pow1` `add-exp-log`
4×	`pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `flip3-+` `frac-add` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
15.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
13.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
29.0ms	(pow (cbrt (cbrt (+ (/ 1 b) (/ 1 a)))) 4)

series444.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
84.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
191.0ms	(pow (cbrt (cbrt (+ (/ 1 b) (/ 1 a)))) 4)

simplify1.4s

Counts

106 → 106

Iterations

Useful iterations: 3 (669.0ms)

Iter	Nodes	Cost
0	168	1776
1	407	1583
2	973	1455
3	3357	1423
done	5000	1423

prune313.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes127.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
done	9	7

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.5s	2541×	body	2560	valid
1.8s	2028×	body	10240	exit
1.8s	3485×	body	1280	valid
301.0ms	1043×	body	640	valid
165.0ms	10030×	pre	80	true
74.0ms	373×	body	320	valid
27.0ms	439×	body	80	valid
15.0ms	121×	body	160	valid