Details

sample474.0ms

Algorithm

intervals

Results

172.0ms	87×	body	2560	valid
95.0ms	60×	body	10240	exit
95.0ms	96×	body	1280	valid
62.0ms	37×	body	640	valid
11.0ms	317×	pre	80	true
4.0ms	12×	body	320	valid
3.0ms	21×	body	80	valid
1.0ms	4×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	258	24
4	760	24
5	3738	24
done	5000	24

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.7b

localize36.0ms

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)))
3.3b	(- (exp (* a eps)) 1.0)
4.4b	(- (exp (* b eps)) 1.0)
6.5b	(- (exp (* (+ a b) eps)) 1.0)

rewrite214.0ms

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:

114.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
27.0ms	(- (exp (* a eps)) 1.0)
36.0ms	(- (exp (* b eps)) 1.0)
29.0ms	(- (exp (* (+ a b) eps)) 1.0)

series519.0ms

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
53.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* b eps)) 1.0)
79.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.5s

Counts

129 → 129

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	228	2725
1	598	2432
2	2209	1949
done	5000	1847

prune629.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite53.0ms

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:

51.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify4.3s

Counts

37 → 37

Iterations

Useful iterations: 3 (248.0ms)

Iter	Nodes	Cost
0	42	245
1	108	231
2	251	211
3	523	210
4	1465	210
5	3712	210
done	5000	210

prune108.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite356.0ms

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:

254.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
27.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
31.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
24.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series556.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
157.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
109.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
124.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify2.1s

Counts

179 → 179

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	182	3562
1	403	3100
2	1000	2944
3	2796	2549
done	5000	2515

prune567.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize5.0ms

Local error

Found 1 expressions with local error:

11.8b

(/ (+ a b) (* a b))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

22.0ms

(/ (+ a b) (* a b))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(/ (+ a b) (* a b))

simplify3.7s

Counts

30 → 30

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	57	304
1	147	298
2	499	256
3	1835	256
done	5000	256

prune67.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes106.0ms

Accuracy

0% (3.2b remaining)

Error of 3.4b against oracle of 0.2b and baseline of 3.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample15.8s

Algorithm

intervals

Results

4.6s	2577×	body	2560	valid
4.5s	3446×	body	1280	valid
3.9s	1986×	body	10240	exit
1.2s	1034×	body	640	valid
558.0ms	451×	body	80	valid
360.0ms	9989×	pre	80	true
153.0ms	374×	body	320	valid
66.0ms	121×	body	160	valid