Details

sample234.0ms

Algorithm

intervals

Results

79.0ms	77×	body	2560	valid
61.0ms	67×	body	10240	exit
56.0ms	115×	body	1280	valid
9.0ms	34×	body	640	valid
5.0ms	323×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	3×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	13
1	101	13
2	258	13
3	766	13
4	3895	13
5	5001	13
done	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.9b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
3.7b	(- (exp (* (+ a b) eps)) 1.0)

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
45×	`prod-diff`
39×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-log-exp`
9×	`flip3--` `fma-neg` `flip--`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`diff-log`
2×	`associate-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 138

Calls

4 calls:

77.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* a eps)) 1.0)
19.0ms	(- (exp (* (+ a b) eps)) 1.0)

series181.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
39.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify63.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	488	1660
1	2051	1241
2	5003	1216
done	5003	1216

prune479.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.0b

localize30.0ms

Local error

Found 4 expressions with local error:

3.2b	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
3.7b	(- (exp (* (+ a b) eps)) 1.0)
13.3b	(* (pow a 2) (pow eps 2))
15.7b	(* (pow a 3) (pow eps 3))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
33×	`unswap-sqr`
30×	`add-exp-log`
28×	`unpow-prod-down`
27×	`prod-diff`
25×	`associate-r`
23×	`associate-l`
20×	`sqr-pow`
19×	`prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-cbrt-cube` `unpow2`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`sub-neg` `fma-neg` `pow-prod-down` `*-commutative` `cbrt-unprod`
2×	`cube-mult` `flip3--` `unpow3` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log`

Counts

4 → 188

Calls

4 calls:

39.0ms	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
16.0ms	(- (exp (* (+ a b) eps)) 1.0)
20.0ms	(* (pow a 2) (pow eps 2))
20.0ms	(* (pow a 3) (pow eps 3))

series288.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
51.0ms	(- (exp (* (+ a b) eps)) 1.0)
39.0ms	(* (pow a 2) (pow eps 2))
64.0ms	(* (pow a 3) (pow eps 3))

simplify119.0ms

Counts

200 → 200

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	651	2054
1	3019	1718
2	5002	1672
done	5002	1672

prune740.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 47.4b

localize25.0ms

Local error

Found 4 expressions with local error:

2.9b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
3.2b	(* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
3.7b	(- (exp (* (+ a b) eps)) 1.0)
13.3b	(* (pow a 2) (pow eps 2))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
30×	`add-exp-log`
29×	`add-cube-cbrt`
27×	`prod-diff`
20×	`add-cbrt-cube`
17×	`unswap-sqr`
14×	`unpow-prod-down` `prod-exp`
13×	`associate-r`
11×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
10×	`unpow2` `sqr-pow`
6×	`pow1` `pow-to-exp` `associate-*r/` `pow-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `flip--` `log1p-expm1-u`
3×	`sub-neg` `fma-neg`
2×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 154

Calls

4 calls:

46.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
41.0ms	(* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
16.0ms	(- (exp (* (+ a b) eps)) 1.0)
18.0ms	(* (pow a 2) (pow eps 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

820.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
113.0ms	(* (fma 1/6 (pow (* eps a) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0))
54.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow a 2) (pow eps 2))

simplify116.0ms

Counts

166 → 166

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	785	2568
1	4065	2039
2	5001	2030
done	5001	2030

prune642.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite40.0ms

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:

39.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify67.0ms

Counts

37 → 37

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	107	112
1	368	101
2	1274	98
3	3144	98
4	5001	98
done	5001	98

prune71.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes67.0ms

Accuracy

0% (3.1b remaining)

Error of 3.1b against oracle of 0.1b and baseline of 3.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3
done	9	3

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2611×	body	2560	valid
1.8s	3447×	body	1280	valid
1.7s	2019×	body	10240	exit
289.0ms	1072×	body	640	valid
157.0ms	10020×	pre	80	true
56.0ms	324×	body	320	valid
21.0ms	422×	body	80	valid
15.0ms	125×	body	160	valid