Details

sample347.0ms

Algorithm

intervals

Results

110.0ms	85×	body	2560	valid
107.0ms	63×	body	10240	exit
72.0ms	97×	body	1280	valid
17.0ms	39×	body	640	valid
7.0ms	319×	pre	80	true
4.0ms	14×	body	320	valid
1.0ms	16×	body	80	valid
1.0ms	5×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b	(- (exp (* b eps)) 1.0)
5.0b	(- (exp (* a eps)) 1.0)
6.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite173.0ms

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:

106.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
23.0ms	(- (exp (* b eps)) 1.0)
16.0ms	(- (exp (* a eps)) 1.0)
18.0ms	(- (exp (* (+ a b) eps)) 1.0)

series310.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
63.0ms	(- (exp (* b eps)) 1.0)
64.0ms	(- (exp (* a eps)) 1.0)
102.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.6s

Counts

150 → 150

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	221	3064
1	488	2615
2	1494	2203
done	5001	2038

prune706.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 47.3b

localize48.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (exp (* a eps)) 1.0)
5.1b	(* (* 1/6 (pow eps 3)) b)
6.6b	(- (exp (* (+ a b) eps)) 1.0)
12.9b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`associate-l`
8×	`add-log-exp`
6×	`pow1` `fma-neg` `associate-r`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `pow-exp` `-commutative` `flip--` `distribute-lft-out--` `unpow2` `difference-of-squares` `sqr-pow`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `flip-+`

Counts

4 → 110

Calls

4 calls:

18.0ms	(- (exp (* a eps)) 1.0)
27.0ms	(* (* 1/6 (pow eps 3)) b)
26.0ms	(- (exp (* (+ a b) eps)) 1.0)
64.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (exp (* a eps)) 1.0)
31.0ms	(* (* 1/6 (pow eps 3)) b)
66.0ms	(- (exp (* (+ a b) eps)) 1.0)
212.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify1.7s

Counts

122 → 122

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	216	2083
1	563	1788
2	1992	1537
done	5000	1463

prune934.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 46.7b

localize34.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (exp (* a eps)) 1.0)
5.1b	(* (* 1/6 (pow eps 3)) b)
6.6b	(- (exp (* (+ a b) eps)) 1.0)
7.8b	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `prod-exp` `add-log-exp`
6×	`fma-neg` `associate-r`
4×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

27.0ms	(- (exp (* a eps)) 1.0)
35.0ms	(* (* 1/6 (pow eps 3)) b)
17.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (exp (* a eps)) 1.0)
51.0ms	(* (* 1/6 (pow eps 3)) b)
76.0ms	(- (exp (* (+ a b) eps)) 1.0)
175.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

simplify1.6s

Counts

111 → 111

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	190	1724
1	430	1515
2	1250	1272
done	5000	1198

prune766.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 46.6b

localize43.0ms

Local error

Found 4 expressions with local error:

5.0b	(- (exp (* a eps)) 1.0)
5.1b	(* (* 1/6 (pow eps 3)) b)
6.6b	(- (exp (* (+ a b) eps)) 1.0)
7.8b	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`prod-diff`
16×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`pow1` `prod-exp` `add-log-exp`
6×	`fma-neg` `associate-r`
4×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `log1p-expm1-u`
2×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `flip--` `fma-udef` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-exp` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

21.0ms	(- (exp (* a eps)) 1.0)
41.0ms	(* (* 1/6 (pow eps 3)) b)
25.0ms	(- (exp (* (+ a b) eps)) 1.0)
8.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(* (* 1/6 (pow eps 3)) b)
74.0ms	(- (exp (* (+ a b) eps)) 1.0)
148.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

simplify1.5s

Counts

111 → 111

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	190	1724
1	430	1515
2	1250	1272
done	5000	1198

prune949.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 46.6b

regimes284.0ms

Accuracy

56.3% (3.5b remaining)

Error of 52.4b against oracle of 48.9b and baseline of 56.9b

bsearch791.0ms

Steps

Iters	Range		Point
9	2.0151688583404304e+101	2.940326713011017e+107	2.0994956295809502e+101
8	-5.625198100549435e+79	-4.694015096128857e+76	-1.2672068894119004e+79

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	49	122
1	66	122
done	66	122

end0.0ms

sample15.3s

Algorithm

intervals

Results

5.4s	2627×	body	2560	valid
4.4s	1999×	body	10240	exit
3.8s	3480×	body	1280	valid
587.0ms	1010×	body	640	valid
321.0ms	10001×	pre	80	true
163.0ms	334×	body	320	valid
42.0ms	434×	body	80	valid
23.0ms	117×	body	160	valid