Details

sample231.0ms

Algorithm

intervals

Results

76.0ms	73×	body	2560	valid
61.0ms	62×	body	10240	exit
56.0ms	112×	body	1280	valid
10.0ms	42×	body	640	valid
5.0ms	318×	pre	80	true
2.0ms	11×	body	320	valid
1.0ms	16×	body	80	valid
0.0ms	2×	body	160	valid

simplify104.0ms

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: 59.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.2b	(- (exp (* b eps)) 1.0)
3.2b	(- (exp (* a eps)) 1.0)
4.9b	(- (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:

73.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
14.0ms	(- (exp (* b eps)) 1.0)
17.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)

series174.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
34.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (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

prune441.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 48.0b

localize32.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (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))
4.9b	(- (exp (* (+ a b) eps)) 1.0)
11.8b	(* (pow a 2) (pow eps 2))
14.7b	(* (pow a 3) (pow eps 3))

rewrite103.0ms

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))
19.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow a 2) (pow eps 2))
20.0ms	(* (pow a 3) (pow eps 3))

series272.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (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)
32.0ms	(* (pow a 2) (pow eps 2))
64.0ms	(* (pow a 3) (pow eps 3))

simplify116.0ms

Counts

200 → 200

Iterations

Useful iterations: 2 (97.0ms)

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

prune717.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 47.8b

localize38.0ms

Local error

Found 4 expressions with local error:

4.9b	(- (exp (* (+ a b) eps)) 1.0)
4.9b	(- (exp (* (+ a b) eps)) 1.0)
11.8b	(* (pow a 2) (pow eps 2))
14.7b	(* (pow a 3) (pow eps 3))

rewrite79.0ms

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:

16.0ms	(- (exp (* (+ a b) eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
21.0ms	(* (pow a 2) (pow eps 2))
21.0ms	(* (pow a 3) (pow eps 3))

series199.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (exp (* (+ a b) eps)) 1.0)
53.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify82.0ms

Counts

182 → 182

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	457	1154
1	2112	907
2	5001	858
done	5001	858

prune803.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 47.8b

localize40.0ms

Local error

Found 4 expressions with local error:

4.9b	(- (exp (* (+ a b) eps)) 1.0)
4.9b	(- (exp (* (+ a b) eps)) 1.0)
11.8b	(* (pow a 2) (pow eps 2))
14.7b	(* (pow a 3) (pow eps 3))

rewrite76.0ms

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:

17.0ms	(- (exp (* (+ a b) eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
17.0ms	(* (pow a 2) (pow eps 2))
20.0ms	(* (pow a 3) (pow eps 3))

series199.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (exp (* (+ a b) eps)) 1.0)
48.0ms	(- (exp (* (+ a b) eps)) 1.0)
32.0ms	(* (pow a 2) (pow eps 2))
65.0ms	(* (pow a 3) (pow eps 3))

simplify83.0ms

Counts

182 → 182

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	457	1154
1	2112	907
2	5001	858
done	5001	858

prune820.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 47.8b

regimes256.0ms

Accuracy

41.4% (5.1b remaining)

Error of 54.0b against oracle of 49.0b and baseline of 57.6b

bsearch307.0ms

Steps

Iters	Range		Point
8	1.3570171099140072e+73	1.3980927165417124e+76	1.6045903834141747e+73
8	-5.309103864954449e+112	-1.0187590636892086e+110	-1.0320051143206996e+110

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	57
1	66	57
done	66	57

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.4s	2511×	body	2560	valid
1.7s	1982×	body	10240	exit
1.7s	3429×	body	1280	valid
299.0ms	1112×	body	640	valid
155.0ms	9984×	pre	80	true
66.0ms	367×	body	320	valid
23.0ms	451×	body	80	valid
15.0ms	132×	body	160	valid