Details

sample396.0ms

Algorithm

intervals

Results

116.0ms	87×	body	10240	exit
105.0ms	78×	body	2560	valid
78.0ms	106×	body	1280	valid
55.0ms	40×	body	640	valid
8.0ms	343×	pre	80	true
2.0ms	8×	body	320	valid
2.0ms	19×	body	80	valid
1.0ms	5×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	245	24
4	699	24
5	3583	24
done	5002	24

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.3b	(- (exp (* b eps)) 1.0)
4.0b	(- (exp (* a eps)) 1.0)
5.2b	(- (exp (* (+ a b) eps)) 1.0)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`flip3--` `flip--`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
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-r/` `associate-l/`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

77.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
18.0ms	(- (exp (* b eps)) 1.0)
12.0ms	(- (exp (* a eps)) 1.0)
14.0ms	(- (exp (* (+ a b) eps)) 1.0)

series201.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
42.0ms	(- (exp (* b eps)) 1.0)
50.0ms	(- (exp (* a eps)) 1.0)
52.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify709.0ms

Counts

88 → 88

Iterations

Useful iterations: done (707.0ms)

Iter	Nodes	Cost
0	143	1364
1	355	1326
2	1635	1198
done	5001	1196

prune486.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 47.4b

localize50.0ms

Local error

Found 4 expressions with local error:

4.0b	(- (exp (* a eps)) 1.0)
5.2b	(- (exp (* (+ a b) eps)) 1.0)
15.1b	(* (pow eps 2) (pow b 2))
17.3b	(* (pow eps 3) (pow b 3))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
32×	`unswap-sqr`
28×	`add-exp-log` `unpow-prod-down`
20×	`associate-r` `associate-l` `sqr-pow`
18×	`*-un-lft-identity` `prod-exp`
14×	`add-cube-cbrt` `cube-prod`
12×	`pow-to-exp` `pow-exp`
10×	`unpow2`
8×	`add-cbrt-cube` `add-log-exp`
4×	`pow1`
2×	`cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 138

Calls

4 calls:

13.0ms	(- (exp (* a eps)) 1.0)
32.0ms	(- (exp (* (+ a b) eps)) 1.0)
38.0ms	(* (pow eps 2) (pow b 2))
40.0ms	(* (pow eps 3) (pow b 3))

series280.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (exp (* a eps)) 1.0)
81.0ms	(- (exp (* (+ a b) eps)) 1.0)
41.0ms	(* (pow eps 2) (pow b 2))
108.0ms	(* (pow eps 3) (pow b 3))

simplify3.0s

Counts

150 → 150

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	207	1707
1	491	1532
2	3186	1328
done	5001	1323

prune960.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 46.6b

localize85.0ms

Local error

Found 4 expressions with local error:

3.6b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
4.0b	(- (exp (* a eps)) 1.0)
5.2b	(- (exp (* (+ a b) eps)) 1.0)
15.1b	(* (pow eps 2) (pow b 2))

rewrite215.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-sqr-sqrt`
18×	`add-cbrt-cube`
16×	`unswap-sqr`
14×	`unpow-prod-down`
13×	`prod-exp`
12×	`*-un-lft-identity`
10×	`unpow2` `sqr-pow`
8×	`add-cube-cbrt` `associate-r` `associate-l` `associate-/r/` `add-log-exp`
6×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
5×	`cbrt-unprod`
4×	`pow1` `cbrt-undiv` `frac-times` `associate-*r/` `div-exp`
3×	`flip3-+` `flip-+`
2×	`sub-neg` `diff-log` `associate-*l/` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `times-frac` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

4 → 110

Calls

4 calls:

147.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
12.0ms	(- (exp (* a eps)) 1.0)
15.0ms	(- (exp (* (+ a b) eps)) 1.0)
36.0ms	(* (pow eps 2) (pow b 2))

series2.4s

Counts

4 → 12

Calls

4 calls:

2.2s	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
45.0ms	(- (exp (* a eps)) 1.0)
75.0ms	(- (exp (* (+ a b) eps)) 1.0)
49.0ms	(* (pow eps 2) (pow b 2))

simplify579.0ms

Counts

122 → 122

Iterations

Useful iterations: done (573.0ms)

Iter	Nodes	Cost
0	250	3081
1	761	2972
done	5000	2368

prune825.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite28.0ms

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` `add-exp-log` `+-commutative` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+`

Counts

1 → 19

Calls

1 calls:

28.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify1.1s

Counts

22 → 22

Iterations

Useful iterations: 3 (269.0ms)

Iter	Nodes	Cost
0	40	229
1	102	216
2	360	196
3	1364	194
done	5001	194

prune50.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes106.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
done	9	7

end0.0ms

sample14.3s

Algorithm

intervals

Results

5.1s	2536×	body	2560	valid
3.6s	1871×	body	10240	exit
3.3s	3467×	body	1280	valid
960.0ms	9873×	pre	80	true
623.0ms	1091×	body	640	valid
122.0ms	336×	body	320	valid
42.0ms	433×	body	80	valid
31.0ms	139×	body	160	valid