Details

sample423.0ms

Algorithm

intervals

Results

137.0ms	88×	body	2560	valid
86.0ms	99×	body	1280	valid
78.0ms	51×	body	10240	exit
61.0ms	307×	pre	80	true
25.0ms	44×	body	640	valid
3.0ms	8×	body	320	valid
2.0ms	16×	body	80	valid
0.0ms	1×	body	160	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	4020
4	765
3	258
2	101
1	40
0	17

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
1.9b	(- (exp (* a eps)) 1.0)
2.1b	(- (exp (* b eps)) 1.0)
3.2b	(- (exp (* (+ a b) eps)) 1.0)

rewrite180.0ms

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-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
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))
23.0ms	(- (exp (* a eps)) 1.0)
33.0ms	(- (exp (* b eps)) 1.0)
23.0ms	(- (exp (* (+ a b) eps)) 1.0)

series246.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
49.0ms	(- (exp (* a eps)) 1.0)
50.0ms	(- (exp (* b eps)) 1.0)
87.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify1.5s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
2	2610
1	540
0	221

prune868.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 49.4b

localize60.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* (pow a 3) (pow eps 3)) 1/6 (fma eps a (* (* a a) (* 1/2 (* eps eps))))) (- (exp (* b eps)) 1.0)))
3.2b	(- (exp (* (+ a b) eps)) 1.0)
15.6b	(* (* a a) (* 1/2 (* eps eps)))
16.6b	(* (pow a 3) (pow eps 3))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log`
43×	`add-sqr-sqrt`
39×	`add-cbrt-cube`
28×	`prod-exp`
25×	`pow1`
20×	`cbrt-unprod`
19×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`pow-prod-down` `unswap-sqr`
14×	`unpow-prod-down` `cube-prod`
13×	`associate-r` `associate-l`
10×	`sqr-pow`
9×	`prod-diff`
6×	`pow-to-exp` `pow-exp` `add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--`
2×	`cube-mult` `unpow3` `associate-/r/` `*-commutative` `associate-/l/`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

43.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* (pow a 3) (pow eps 3)) 1/6 (fma eps a (* (* a a) (* 1/2 (* eps eps))))) (- (exp (* b eps)) 1.0)))
23.0ms	(- (exp (* (+ a b) eps)) 1.0)
60.0ms	(* (* a a) (* 1/2 (* eps eps)))
32.0ms	(* (pow a 3) (pow eps 3))

series1.8s

Counts

4 → 12

Calls

4 calls:

1.6s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* (pow a 3) (pow eps 3)) 1/6 (fma eps a (* (* a a) (* 1/2 (* eps eps))))) (- (exp (* b eps)) 1.0)))
62.0ms	(- (exp (* (+ a b) eps)) 1.0)
62.0ms	(* (* a a) (* 1/2 (* eps eps)))
92.0ms	(* (pow a 3) (pow eps 3))

simplify458.0ms

Counts

158 → 158

Iterations

Iter	Nodes
done	5001
1	915
0	293

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ (/ 1 a) (/ 1 b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`times-frac`
13×	`fma-def`
10×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`distribute-lft-out`
5×	`div-inv`
3×	`add-log-exp`
1×	`expm1-log1p-u` `pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

28.0ms

(+ (/ 1 a) (/ 1 b))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(+ (/ 1 a) (/ 1 b))

simplify2.2s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
3	2236
2	439
1	110
0	42

prune218.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
0.6b	(cbrt (/ 1 a))
0.6b	(cbrt (/ 1 a))
0.6b	(cbrt (/ 1 a))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

119×	`cbrt-prod`
97×	`add-sqr-sqrt`
79×	`times-frac`
67×	`*-un-lft-identity`
57×	`add-cube-cbrt`
18×	`swap-sqr`
16×	`associate-r` `associate-l` `unswap-sqr`
11×	`pow1`
9×	`pow1/3` `div-inv`
7×	`cbrt-div`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 161

Calls

4 calls:

27.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
2.0ms	(cbrt (/ 1 a))
4.0ms	(cbrt (/ 1 a))
4.0ms	(cbrt (/ 1 a))

series1.1s

Counts

4 → 12

Calls

4 calls:

299.0ms	(* (cbrt (/ 1 a)) (cbrt (/ 1 a)))
269.0ms	(cbrt (/ 1 a))
268.0ms	(cbrt (/ 1 a))
294.0ms	(cbrt (/ 1 a))

simplify1.3s

Counts

173 → 173

Iterations

Iter	Nodes
done	5001
2	1088
1	255
0	143

prune704.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes158.0ms

Accuracy

0% (3.1b remaining)

Error of 3.2b against oracle of 0.1b and baseline of 3.2b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample16.0s

Algorithm

intervals

Results

5.6s	2553×	body	2560	valid
4.4s	2011×	body	10240	exit
4.1s	3518×	body	1280	valid
771.0ms	1057×	body	640	valid
271.0ms	10013×	pre	80	true
154.0ms	328×	body	320	valid
63.0ms	115×	body	160	valid
45.0ms	431×	body	80	valid