Details

sample333.0ms

Algorithm

intervals

Results

110.0ms	73×	body	2560	valid
94.0ms	117×	body	1280	valid
70.0ms	52×	body	10240	exit
15.0ms	36×	body	640	valid
13.0ms	308×	pre	80	true
2.0ms	8×	body	320	valid
1.0ms	18×	body	80	valid
1.0ms	4×	body	160	valid

simplify3.4s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.7b	(- (exp (* b eps)) 1.0)
2.8b	(- (exp (* a eps)) 1.0)
4.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite204.0ms

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:

116.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
30.0ms	(- (exp (* b eps)) 1.0)
27.0ms	(- (exp (* a eps)) 1.0)
20.0ms	(- (exp (* (+ a b) eps)) 1.0)

series275.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
45.0ms	(- (exp (* b eps)) 1.0)
53.0ms	(- (exp (* a eps)) 1.0)
86.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.1s

Counts

150 → 150

Iterations

Useful iterations: done (1.1s)

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

prune711.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 48.1b

localize64.0ms

Local error

Found 4 expressions with local error:

2.8b	(- (exp (* a eps)) 1.0)
3.6b	(* (* 1/6 (pow eps 3)) b)
4.4b	(- (exp (* (+ a b) eps)) 1.0)
12.0b	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

rewrite156.0ms

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:

26.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(* (* 1/6 (pow eps 3)) b)
23.0ms	(- (exp (* (+ a b) eps)) 1.0)
67.0ms	(* (pow b 2) (+ (* 1/2 (pow eps 2)) (* (* 1/6 (pow eps 3)) b)))

series331.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (exp (* a eps)) 1.0)
48.0ms	(* (* 1/6 (pow eps 3)) b)
91.0ms	(- (exp (* (+ a b) eps)) 1.0)
151.0ms	(* (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

prune909.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 47.7b

localize42.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (* 1/6 (pow eps 3)) b)
4.4b	(- (exp (* (+ a b) eps)) 1.0)
4.7b	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
5.0b	(* (pow b (/ 2 2)) (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 101

Calls

4 calls:

46.0ms	(* (* 1/6 (pow eps 3)) b)
33.0ms	(- (exp (* (+ a b) eps)) 1.0)
14.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
44.0ms	(* (pow b (/ 2 2)) (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))

series367.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (* 1/6 (pow eps 3)) b)
66.0ms	(- (exp (* (+ a b) eps)) 1.0)
122.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
151.0ms	(* (pow b (/ 2 2)) (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	198	2085
1	472	1796
2	1446	1509
done	5001	1465

prune785.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 47.7b

localize71.0ms

Local error

Found 4 expressions with local error:

4.4b	(- (exp (* (+ a b) eps)) 1.0)
4.4b	(log (exp (- (exp (* (+ a b) eps)) 1.0)))
4.7b	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
5.0b	(* (pow b (/ 2 2)) (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
23×	`add-cube-cbrt`
19×	`add-exp-log`
18×	`prod-diff`
14×	`log-prod`
11×	`exp-sum` `add-cbrt-cube`
10×	`associate-l` `prod-exp`
7×	`pow1`
6×	`log-pow` `fma-udef` `add-log-exp`
5×	`distribute-rgt-in` `exp-prod` `distribute-lft-in`
4×	`expm1-log1p-u` `associate-r` `cbrt-unprod` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-neg`
2×	`pow-to-exp` `sub-neg` `pow-exp` `*-commutative` `distribute-lft-out--` `difference-of-squares`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 111

Calls

4 calls:

33.0ms	(- (exp (* (+ a b) eps)) 1.0)
66.0ms	(log (exp (- (exp (* (+ a b) eps)) 1.0)))
15.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
46.0ms	(* (pow b (/ 2 2)) (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))

series450.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (exp (* (+ a b) eps)) 1.0)
60.0ms	(log (exp (- (exp (* (+ a b) eps)) 1.0)))
150.0ms	(* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b)))
153.0ms	(* (pow b (/ 2 2)) (* b (fma 1/2 (pow eps 2) (* (* 1/6 (pow eps 3)) b))))

simplify4.0s

Counts

123 → 123

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	217	2508
1	442	2080
2	1069	1727
3	4622	1620
done	5000	1618

prune859.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 47.7b

regimes384.0ms

Accuracy

51.6% (3.8b remaining)

Error of 52.3b against oracle of 48.5b and baseline of 56.4b

bsearch694.0ms

Steps

Iters	Range	Point
7	1.5508478278740396e+18	5.540055658358989e+19	1.1675070506728612e+19
9	-6.913431520583017e+89	-5.532268721092573e+81	-5.831284548290567e+81
8	-1.254023704673695e+179	-2.1235528112433396e+175	-7.755384029378696e+176

Iters

Range

Point

1.5508478278740396e+18

5.540055658358989e+19

1.1675070506728612e+19

-6.913431520583017e+89

-5.532268721092573e+81

-5.831284548290567e+81

-1.254023704673695e+179

-2.1235528112433396e+175

-7.755384029378696e+176

simplify33.0ms

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	55	163
1	73	159
2	75	155
done	75	155

end0.0ms

sample10.2s

Algorithm

intervals

Results

3.6s	2571×	body	2560	valid
2.6s	3483×	body	1280	valid
2.5s	1948×	body	10240	exit
445.0ms	1054×	body	640	valid
244.0ms	9949×	pre	80	true
93.0ms	332×	body	320	valid
35.0ms	448×	body	80	valid
25.0ms	113×	body	160	valid