Details

sample223.0ms

Algorithm

intervals

Results

81.0ms	87×	body	2560	valid
53.0ms	60×	body	10240	exit
45.0ms	90×	body	1280	valid
11.0ms	41×	body	640	valid
10.0ms	316×	pre	80	true
3.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid
1.0ms	15×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	252	24
4	711	24
5	3280	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.8b

localize21.0ms

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)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
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 → 117

Calls

4 calls:

23.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* a eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series328.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
33.0ms	(- (exp (* b eps)) 1.0)
35.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.1s

Counts

129 → 129

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	228	2725
1	608	2432
2	2327	1949
done	5001	1922

prune440.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

18.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify2.5s

Counts

37 → 37

Iterations

Useful iterations: 3 (120.0ms)

Iter	Nodes	Cost
0	42	245
1	108	231
2	244	211
3	570	210
4	1251	210
5	3154	210
done	5000	210

prune88.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

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)))

rewrite174.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 167

Calls

4 calls:

122.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series352.0ms

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)))
83.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
85.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify1.9s

Counts

179 → 179

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	182	3562
1	404	3132
2	1084	2925
3	3674	2535
done	5000	2527

prune351.0ms

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)

rewrite80.0ms

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×	`expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `flip3-+` `frac-add` `flip-+`
2×	`pow-pow`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
16.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
14.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
31.0ms	(pow (cbrt (cbrt (+ (/ 1 b) (/ 1 a)))) 4)

series459.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
87.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
87.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
197.0ms	(pow (cbrt (cbrt (+ (/ 1 b) (/ 1 a)))) 4)

simplify2.2s

Counts

114 → 114

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	172	1854
1	419	1696
2	1043	1540
3	3560	1494
done	5000	1490

prune336.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes122.0ms

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

sample6.9s

Algorithm

intervals

Results

2.5s	2541×	body	2560	valid
1.8s	2028×	body	10240	exit
1.7s	3485×	body	1280	valid
286.0ms	1043×	body	640	valid
169.0ms	10030×	pre	80	true
72.0ms	373×	body	320	valid
24.0ms	439×	body	80	valid
14.0ms	121×	body	160	valid