Details

sample409.0ms

Algorithm

intervals

Results

126.0ms	109×	body	1280	valid
117.0ms	80×	body	2560	valid
94.0ms	71×	body	10240	exit
18.0ms	6×	body	320	valid
15.0ms	38×	body	640	valid
8.0ms	328×	pre	80	true
2.0ms	19×	body	80	valid
1.0ms	5×	body	160	valid

simplify2.6s

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	765	24
5	4008	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.5b	(- (exp (* b eps)) 1.0)
5.3b	(- (exp (* a eps)) 1.0)
7.2b	(- (exp (* (+ a b) eps)) 1.0)

rewrite192.0ms

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:

110.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
18.0ms	(- (exp (* a eps)) 1.0)
22.0ms	(- (exp (* (+ a b) eps)) 1.0)

series208.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
34.0ms	(- (exp (* b eps)) 1.0)
37.0ms	(- (exp (* a eps)) 1.0)
70.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify2.1s

Counts

150 → 150

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	221	3064
1	539	2630
2	2593	2205
done	5001	2041

prune628.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 48.9b

localize48.0ms

Local error

Found 4 expressions with local error:

5.3b	(- (exp (* a eps)) 1.0)
7.2b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))
17.3b	(* (pow eps 3) (pow b 3))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `unswap-sqr`
28×	`add-exp-log` `add-cube-cbrt` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`prod-diff` `prod-exp`
14×	`cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
6×	`fma-neg`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

22.0ms	(- (exp (* a eps)) 1.0)
22.0ms	(- (exp (* (+ a b) eps)) 1.0)
18.0ms	(* (pow eps 2) (pow b 2))
30.0ms	(* (pow eps 3) (pow b 3))

series273.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (exp (* a eps)) 1.0)
54.0ms	(- (exp (* (+ a b) eps)) 1.0)
54.0ms	(* (pow eps 2) (pow b 2))
101.0ms	(* (pow eps 3) (pow b 3))

simplify2.8s

Counts

182 → 182

Iterations

Useful iterations: 2 (796.0ms)

Iter	Nodes	Cost
0	250	2347
1	598	2012
2	3522	1688
done	5000	1688

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 48.3b

localize66.0ms

Local error

Found 4 expressions with local error:

2.3b	(fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))
5.3b	(- (exp (* a eps)) 1.0)
7.2b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

1.0ms	(fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))
28.0ms	(- (exp (* a eps)) 1.0)
18.0ms	(- (exp (* (+ a b) eps)) 1.0)
18.0ms	(* (pow eps 2) (pow b 2))

series307.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))
49.0ms	(- (exp (* a eps)) 1.0)
83.0ms	(- (exp (* (+ a b) eps)) 1.0)
41.0ms	(* (pow eps 2) (pow b 2))

simplify2.0s

Counts

131 → 131

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	206	1936
1	473	1684
2	2360	1343
done	5001	1261

prune824.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 48.3b

localize87.0ms

Local error

Found 4 expressions with local error:

2.3b	(fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))
5.3b	(- (exp (* a eps)) 1.0)
7.2b	(- (exp (* (+ a b) eps)) 1.0)
14.5b	(* (pow eps 2) (pow b 2))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

1.0ms	(fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))
37.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(- (exp (* (+ a b) eps)) 1.0)
35.0ms	(* (pow eps 2) (pow b 2))

series327.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))
52.0ms	(- (exp (* a eps)) 1.0)
63.0ms	(- (exp (* (+ a b) eps)) 1.0)
45.0ms	(* (pow eps 2) (pow b 2))

simplify2.0s

Counts

131 → 131

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	206	1936
1	473	1684
2	2360	1343
done	5001	1261

prune888.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 48.3b

regimes340.0ms

Accuracy

33.2% (5.7b remaining)

Error of 54.6b against oracle of 48.9b and baseline of 57.4b

bsearch1.1s

Steps

Iters	Range	Point
9	1.0609078318365286e+52	2.910271384286922e+60	1.3507332008538112e+52
9	-2.7212884249074652e+69	-2.141455312889249e+62	-1.4289229802522745e+68
10	-5.925035818637428e+242	-1.3186852967682748e+232	-3.1084886035262666e+235

Iters

Range

Point

1.0609078318365286e+52

2.910271384286922e+60

1.3507332008538112e+52

-2.7212884249074652e+69

-2.141455312889249e+62

-1.4289229802522745e+68

-5.925035818637428e+242

-1.3186852967682748e+232

-3.1084886035262666e+235

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	54	169
1	65	169
done	65	169

end0.0ms

sample15.8s

Algorithm

intervals

Results

5.1s	2043×	body	10240	exit
4.7s	2475×	body	2560	valid
3.6s	3529×	body	1280	valid
931.0ms	10044×	pre	80	true
645.0ms	1102×	body	640	valid
108.0ms	302×	body	320	valid
47.0ms	455×	body	80	valid
31.0ms	138×	body	160	valid