Details

sample464.0ms

Algorithm

intervals

Results

168.0ms	73×	body	10240	exit
143.0ms	90×	body	2560	valid
86.0ms	105×	body	1280	valid
16.0ms	29×	body	640	valid
9.0ms	329×	pre	80	true
4.0ms	11×	body	320	valid
2.0ms	16×	body	80	valid
1.0ms	5×	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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.6b

localize42.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.1b	(- (exp (* b eps)) 1.0)
3.4b	(- (exp (* a eps)) 1.0)
5.4b	(- (exp (* (+ a b) eps)) 1.0)

rewrite137.0ms

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:

82.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
18.0ms	(- (exp (* b eps)) 1.0)
19.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series259.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
51.0ms	(- (exp (* b eps)) 1.0)
44.0ms	(- (exp (* a eps)) 1.0)
87.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify777.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1625
1	356
0	143

prune736.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 48.7b

localize78.0ms

Local error

Found 4 expressions with local error:

4.8b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* eps eps) 1/2) (* a a)) (* eps a)) (* (* (pow a 3) 1/6) (pow eps 3))) (- (exp (* b eps)) 1.0)))
5.4b	(- (exp (* (+ a b) eps)) 1.0)
13.2b	(* (* (* eps eps) 1/2) (* a a))
15.6b	(* (* (pow a 3) 1/6) (pow eps 3))

rewrite458.0ms

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:

326.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* eps eps) 1/2) (* a a)) (* eps a)) (* (* (pow a 3) 1/6) (pow eps 3))) (- (exp (* b eps)) 1.0)))
11.0ms	(- (exp (* (+ a b) eps)) 1.0)
68.0ms	(* (* (* eps eps) 1/2) (* a a))
45.0ms	(* (* (pow a 3) 1/6) (pow eps 3))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (+ (* (* (* eps eps) 1/2) (* a a)) (* eps a)) (* (* (pow a 3) 1/6) (pow eps 3))) (- (exp (* b eps)) 1.0)))
61.0ms	(- (exp (* (+ a b) eps)) 1.0)
65.0ms	(* (* (* eps eps) 1/2) (* a a))
96.0ms	(* (* (pow a 3) 1/6) (pow eps 3))

simplify563.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
1	907
0	272

prune883.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 1 expressions with local error:

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

rewrite23.0ms

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:

22.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify1.3s

Counts

22 → 22

Iterations

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

prune129.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite323.0ms

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:

239.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
17.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
36.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
17.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
142.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
129.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))
112.0ms	(cbrt (+ (/ 1 b) (/ 1 a)))

simplify1.4s

Counts

171 → 171

Iterations

Iter	Nodes
done	5000
2	1903
1	425
0	178

prune634.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes390.0ms

Accuracy

89% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 3.2b

bsearch5.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	39
1	39
0	27

end0.0ms

sample16.2s

Algorithm

intervals

Results

5.0s	2615×	body	2560	valid
4.3s	3397×	body	1280	valid
3.9s	1968×	body	10240	exit
1.1s	1066×	body	640	valid
882.0ms	9969×	pre	80	true
180.0ms	354×	body	320	valid
117.0ms	436×	body	80	valid
32.0ms	133×	body	160	valid