Details

sample213.0ms

Algorithm

intervals

Results

76.0ms	83×	body	2560	valid
53.0ms	111×	body	1280	valid
47.0ms	59×	body	10240	exit
9.0ms	36×	body	640	valid
5.0ms	315×	pre	80	true
1.0ms	8×	body	320	valid
1.0ms	15×	body	80	valid
0.0ms	3×	body	160	valid

simplify101.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.3b	(- (exp (* b eps)) 1.0)
3.5b	(- (exp (* a eps)) 1.0)
5.5b	(- (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 (* b eps)) 1.0)
14.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series177.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
33.0ms	(- (exp (* b eps)) 1.0)
40.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify67.0ms

Counts

150 → 150

Iterations

Useful iterations: 2 (50.0ms)

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

prune480.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 52.0b

localize29.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (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)))
5.5b	(- (exp (* (+ a b) eps)) 1.0)
12.9b	(* (pow a 2) (pow eps 2))
14.3b	(* (pow a 3) (pow eps 3))

rewrite109.0ms

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` `associate-*r/` `div-exp` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `pow-prod-down` `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:

45.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (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)))
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow a 2) (pow eps 2))
24.0ms	(* (pow a 3) (pow eps 3))

series1.0s

Counts

4 → 12

Calls

4 calls:

854.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (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)))
56.0ms	(- (exp (* (+ a b) eps)) 1.0)
34.0ms	(* (pow a 2) (pow eps 2))
71.0ms	(* (pow a 3) (pow eps 3))

simplify132.0ms

Counts

181 → 181

Iterations

Useful iterations: 2 (115.0ms)

Iter	Nodes	Cost
0	790	1822
1	4490	1421
2	5001	1416
done	5001	1416

prune765.0ms

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))

rewrite31.0ms

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:

30.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify71.0ms

Counts

37 → 37

Iterations

Useful iterations: 2 (12.0ms)

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

prune92.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

14.4b

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

rewrite22.0ms

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:

21.0ms

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

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

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

simplify49.0ms

Counts

30 → 30

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	149	142
1	531	120
2	2110	120
3	5001	120
done	5001	120

prune45.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes94.0ms

Accuracy

0% (3.2b remaining)

Error of 3.5b against oracle of 0.3b 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

sample6.8s

Algorithm

intervals

Results

2.5s	2620×	body	2560	valid
1.8s	2023×	body	10240	exit
1.6s	3374×	body	1280	valid
285.0ms	1074×	body	640	valid
150.0ms	10024×	pre	80	true
60.0ms	338×	body	320	valid
24.0ms	469×	body	80	valid
17.0ms	126×	body	160	valid