Details

sample218.0ms

Algorithm

intervals

Results

83.0ms	90×	body	2560	valid
49.0ms	55×	body	10240	exit
49.0ms	102×	body	1280	valid
9.0ms	35×	body	640	valid
5.0ms	311×	pre	80	true
2.0ms	13×	body	320	valid
1.0ms	13×	body	80	valid
0.0ms	3×	body	160	valid

simplify98.0ms

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: 60.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* a eps)) 1.0)
3.0b	(- (exp (* b eps)) 1.0)
4.8b	(- (exp (* (+ a b) eps)) 1.0)

rewrite124.0ms

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:

76.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series169.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
37.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(- (exp (* b eps)) 1.0)
49.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify63.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (48.0ms)

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

prune446.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 50.1b

localize27.0ms

Local error

Found 4 expressions with local error:

4.2b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
4.8b	(- (exp (* (+ a b) eps)) 1.0)
14.0b	(* (pow eps 2) (pow b 2))
15.8b	(* (pow eps 3) (pow b 3))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
40×	`add-exp-log`
32×	`unswap-sqr`
28×	`unpow-prod-down`
23×	`*-un-lft-identity`
22×	`prod-exp`
21×	`add-cube-cbrt`
20×	`associate-r` `associate-l` `add-cbrt-cube` `sqr-pow`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
9×	`prod-diff`
6×	`cbrt-unprod` `add-log-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `*-commutative` `associate-/l/`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 169

Calls

4 calls:

49.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
16.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow eps 2) (pow b 2))
22.0ms	(* (pow eps 3) (pow b 3))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.5s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
52.0ms	(- (exp (* (+ a b) eps)) 1.0)
33.0ms	(* (pow eps 2) (pow b 2))
65.0ms	(* (pow eps 3) (pow b 3))

simplify133.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	785	1816
1	4673	1415
2	5001	1412
done	5001	1412

prune694.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize4.0ms

Local error

Found 1 expressions with local error:

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

rewrite25.0ms

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:

23.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify68.0ms

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

prune79.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt b) (cbrt b))
0.6b	(cbrt b)
0.6b	(cbrt b)
0.6b	(cbrt b)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

13.0ms	(* (cbrt b) (cbrt b))
1.0ms	(cbrt b)
1.0ms	(cbrt b)
1.0ms	(cbrt b)

series733.0ms

Counts

4 → 12

Calls

4 calls:

209.0ms	(* (cbrt b) (cbrt b))
172.0ms	(cbrt b)
175.0ms	(cbrt b)
176.0ms	(cbrt b)

simplify88.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	255
done	5001	255

prune237.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes85.0ms

Accuracy

0% (3.3b remaining)

Error of 3.5b against oracle of 0.1b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	2609×	body	2560	valid
1.7s	2039×	body	10240	exit
1.6s	3403×	body	1280	valid
278.0ms	1053×	body	640	valid
144.0ms	10041×	pre	80	true
58.0ms	340×	body	320	valid
23.0ms	464×	body	80	valid
15.0ms	133×	body	160	valid