Details

sample381.0ms

Algorithm

intervals

Results

146.0ms	88×	body	2560	valid
87.0ms	51×	body	10240	exit
83.0ms	99×	body	1280	valid
24.0ms	44×	body	640	valid
8.0ms	307×	pre	80	true
3.0ms	8×	body	320	valid
2.0ms	16×	body	80	valid
0.0ms	1×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3569
4	699
3	245
2	101
1	40
0	17

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 60.0b

localize27.0ms

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)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`sub-neg` `associate-r` `associate-l` `distribute-lft-out--` `difference-of-squares`
4×	`frac-times`
3×	`diff-log`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

67.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
19.0ms	(- (exp (* a eps)) 1.0)
18.0ms	(- (exp (* b eps)) 1.0)
26.0ms	(- (exp (* (+ a b) eps)) 1.0)

series223.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
41.0ms	(- (exp (* a eps)) 1.0)
42.0ms	(- (exp (* b eps)) 1.0)
69.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify809.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1781
1	359
0	143

prune692.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 49.4b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
42×	`add-cbrt-cube`
40×	`prod-exp`
25×	`pow1`
22×	`cbrt-unprod`
15×	`pow-prod-down`
13×	`associate-r`
9×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`associate-/r/`
7×	`pow-to-exp` `pow-exp` `add-cube-cbrt`
6×	`add-log-exp`
5×	`flip3--` `flip--`
4×	`frac-times` `cbrt-undiv` `div-exp` `associate-*r/`
3×	`unpow-prod-down` `flip3-+` `cube-prod` `flip-+`
2×	`associate-l` `associate-l/` `-commutative` `associate-/l/`
1×	`cube-mult` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `times-frac` `diff-log` `unpow3` `div-inv` `associate-/l` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

114.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* 1/6 (pow a 3)) (pow eps 3)) (* eps a)) (* (* a a) (* (* eps eps) 1/2))) (- (exp (* b eps)) 1.0)))
10.0ms	(- (exp (* (+ a b) eps)) 1.0)
56.0ms	(* (* a a) (* (* eps eps) 1/2))
24.0ms	(* (* 1/6 (pow a 3)) (pow eps 3))

series1.5s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* 1/6 (pow a 3)) (pow eps 3)) (* eps a)) (* (* a a) (* (* eps eps) 1/2))) (- (exp (* b eps)) 1.0)))
84.0ms	(- (exp (* (+ a b) eps)) 1.0)
71.0ms	(* (* a a) (* (* eps eps) 1/2))
123.0ms	(* (* 1/6 (pow a 3)) (pow eps 3))

simplify589.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
1	912
0	271

prune851.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
7×	`distribute-lft-out`
6×	`times-frac`
4×	`div-inv`
3×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
1×	`pow1` `+-commutative` `sum-log` `flip3-+` `add-cbrt-cube` `frac-add` `add-exp-log` `flip-+`

Counts

1 → 19

Calls

1 calls:

19.0ms

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

series12.0ms

Counts

1 → 3

Calls

1 calls:

12.0ms

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

simplify1.1s

Counts

22 → 22

Iterations

Iter	Nodes
done	5000
3	1500
2	381
1	102
0	40

prune79.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

139×	`*-un-lft-identity`
114×	`cbrt-prod`
81×	`distribute-lft-out`
60×	`div-inv`
42×	`times-frac`
37×	`add-sqr-sqrt`
33×	`cbrt-div` `swap-sqr`
29×	`add-cube-cbrt`
13×	`associate-r` `associate-l`
11×	`pow1` `flip3-+` `frac-add` `flip-+`
9×	`frac-times` `pow1/3`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`associate-l/` `associate-r/`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 159

Calls

4 calls:

213.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
26.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
24.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
23.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

series494.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (cbrt (+ (/ 1 a) (/ 1 b))) (cbrt (+ (/ 1 a) (/ 1 b))))
98.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
139.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))
120.0ms	(cbrt (+ (/ 1 a) (/ 1 b)))

simplify1.2s

Counts

171 → 171

Iterations

Iter	Nodes
done	5001
2	1902
1	426
0	178

prune742.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes165.0ms

Accuracy

0% (3.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample16.4s

Algorithm

intervals

Results

5.8s	2553×	body	2560	valid
4.4s	2011×	body	10240	exit
3.8s	3518×	body	1280	valid
849.0ms	10013×	pre	80	true
670.0ms	1057×	body	640	valid
134.0ms	328×	body	320	valid
48.0ms	431×	body	80	valid
28.0ms	115×	body	160	valid