Details

sample355.0ms

Algorithm

intervals

Results

102.0ms	67×	body	2560	valid
100.0ms	117×	body	1280	valid
86.0ms	50×	body	10240	exit
19.0ms	37×	body	640	valid
8.0ms	306×	pre	80	true
5.0ms	13×	body	320	valid
2.0ms	18×	body	80	valid
1.0ms	4×	body	160	valid

simplify3.8s

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	760	24
5	3738	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.3b

localize33.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
2.7b	(- (exp (* a eps)) 1.0)
4.1b	(- (exp (* (+ a b) eps)) 1.0)

rewrite177.0ms

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:

96.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
32.0ms	(- (exp (* b eps)) 1.0)
15.0ms	(- (exp (* a eps)) 1.0)
29.0ms	(- (exp (* (+ a b) eps)) 1.0)

series247.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
43.0ms	(- (exp (* b eps)) 1.0)
56.0ms	(- (exp (* a eps)) 1.0)
73.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.2s

Counts

150 → 150

Iterations

Useful iterations: done (1.2s)

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

prune677.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 48.7b

localize56.0ms

Local error

Found 4 expressions with local error:

2.7b	(- (exp (* a eps)) 1.0)
3.1b	(* (* 1/6 (pow eps 3)) b)
4.1b	(- (exp (* (+ a b) eps)) 1.0)
13.0b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite149.0ms

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:

30.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(* (* 1/6 (pow eps 3)) b)
16.0ms	(- (exp (* (+ a b) eps)) 1.0)
63.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (exp (* a eps)) 1.0)
37.0ms	(* (* 1/6 (pow eps 3)) b)
83.0ms	(- (exp (* (+ a b) eps)) 1.0)
203.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify1.8s

Counts

122 → 122

Iterations

Useful iterations: done (1.8s)

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

prune934.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 47.6b

localize71.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (* 1/6 (pow eps 3)) b)
4.1b	(- (exp (* (+ a b) eps)) 1.0)
5.1b	(* b (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))
5.7b	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log`
19×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`add-cbrt-cube`
15×	`add-cube-cbrt`
13×	`pow1`
11×	`prod-exp`
9×	`prod-diff`
7×	`associate-r` `associate-l` `cbrt-unprod`
6×	`fma-udef` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `*-commutative`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

29.0ms	(* (* 1/6 (pow eps 3)) b)
27.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* b (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))
14.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* 1/6 (pow eps 3)) b)
83.0ms	(- (exp (* (+ a b) eps)) 1.0)
178.0ms	(* b (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))
174.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))

simplify1.5s

Counts

107 → 107

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	180	1815
1	412	1674
2	1318	1408
done	5000	1363

prune804.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 47.6b

localize38.0ms

Local error

Found 4 expressions with local error:

3.1b	(* (* 1/6 (pow eps 3)) b)
4.1b	(- (exp (* (+ a b) eps)) 1.0)
4.3b	(* (- (pow (exp a) eps) 1.0) (fma b eps (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))))
13.0b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

49.0ms	(* (* 1/6 (pow eps 3)) b)
33.0ms	(- (exp (* (+ a b) eps)) 1.0)
142.0ms	(* (- (pow (exp a) eps) 1.0) (fma b eps (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))))
54.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series631.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 1/6 (pow eps 3)) b)
76.0ms	(- (exp (* (+ a b) eps)) 1.0)
331.0ms	(* (- (pow (exp a) eps) 1.0) (fma b eps (* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))))
194.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

simplify2.0s

Counts

122 → 122

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	248	2690
1	647	2436
2	2534	2152
done	5002	2086

prune932.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 44.4b

regimes337.0ms

Accuracy

45.8% (4.8b remaining)

Error of 50.6b against oracle of 45.9b and baseline of 54.7b

bsearch759.0ms

Steps

Iters	Range		Point
10	1.2079217355322146e+29	2.856332945856771e+44	1.0050381620843746e+41
8	-48121633144.00611	-68825036.81334019	-173005857.23040006

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	52	128
1	72	88
done	72	88

end0.0ms

sample15.4s

Algorithm

intervals

Results

4.9s	3530×	body	1280	valid
4.4s	2528×	body	2560	valid
4.2s	1971×	body	10240	exit
606.0ms	1025×	body	640	valid
554.0ms	9977×	pre	80	true
120.0ms	365×	body	320	valid
47.0ms	449×	body	80	valid
24.0ms	109×	body	160	valid