Details

sample210.0ms

Algorithm

intervals

Results

73.0ms	77×	body	2560	valid
59.0ms	116×	body	1280	valid
43.0ms	54×	body	10240	exit
10.0ms	37×	body	640	valid
5.0ms	310×	pre	80	true
1.0ms	7×	body	320	valid
1.0ms	19×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	40	24
2	101	24
3	253	24
4	722	24
5	3337	24
done	5000	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
3.6b	(- (exp (* a eps)) 1.0)
4.8b	(- (exp (* b eps)) 1.0)
7.6b	(- (exp (* (+ a b) eps)) 1.0)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
25×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`flip3--` `flip--` `add-log-exp`
9×	`fma-neg`
8×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`
2×	`associate-*l/` `associate-/l/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 117

Calls

4 calls:

22.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
5.0ms	(- (exp (* a eps)) 1.0)
8.0ms	(- (exp (* b eps)) 1.0)
5.0ms	(- (exp (* (+ a b) eps)) 1.0)

series301.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0)))
33.0ms	(- (exp (* a eps)) 1.0)
34.0ms	(- (exp (* b eps)) 1.0)
46.0ms	(- (exp (* (+ a b) eps)) 1.0)

simplify965.0ms

Counts

129 → 129

Iterations

Useful iterations: 2 (207.0ms)

Iter	Nodes	Cost
0	228	2725
1	619	2432
2	2661	1922
done	5000	1922

prune429.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite21.0ms

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×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `frac-add` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u`

Counts

1 → 34

Calls

1 calls:

20.0ms

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

series10.0ms

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify2.1s

Counts

37 → 37

Iterations

Useful iterations: 3 (210.0ms)

Iter	Nodes	Cost
0	42	245
1	108	231
2	376	211
3	1016	210
4	1978	210
done	5000	210

prune87.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize4.0ms

Local error

Found 1 expressions with local error:

15.0b

(/ (+ a b) (* a b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`times-frac` `associate-/l*`
3×	`add-sqr-sqrt` `add-cube-cbrt`
2×	`cbrt-undiv` `div-exp` `associate-/l/` `distribute-lft-out`
1×	`pow1` `expm1-log1p-u` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 27

Calls

1 calls:

9.0ms

(/ (+ a b) (* a b))

series38.0ms

Counts

1 → 3

Calls

1 calls:

38.0ms

(/ (+ a b) (* a b))

simplify667.0ms

Counts

30 → 30

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	57	304
1	149	298
2	484	256
3	1727	256
done	5000	256

prune61.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ a b) b)
4.6b	(* (/ 1 a) (/ (+ a b) b))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
40×	`times-frac`
26×	`add-exp-log` `add-cube-cbrt`
16×	`associate-r` `add-cbrt-cube`
13×	`associate-l`
9×	`div-exp`
8×	`prod-exp`
7×	`distribute-lft-out`
6×	`unswap-sqr`
5×	`cbrt-undiv`
4×	`pow1` `cbrt-unprod` `associate-/l*`
3×	`associate-/r*` `div-inv`
2×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip-+`

Counts

2 → 96

Calls

2 calls:

8.0ms	(/ (+ a b) b)
23.0ms	(* (/ 1 a) (/ (+ a b) b))

series54.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(/ (+ a b) b)
38.0ms	(* (/ 1 a) (/ (+ a b) b))

simplify919.0ms

Counts

102 → 102

Iterations

Useful iterations: 2 (151.0ms)

Iter	Nodes	Cost
0	144	1177
1	409	1047
2	1690	901
done	5000	901

prune158.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes99.0ms

Accuracy

-46.9% (4.7b remaining)

Error of 4.8b against oracle of 0.1b and baseline of 3.3b

bsearch85.0ms

Steps

Iters	Range		Point
5	1.9693570888132737e-31	5.4209506770775015e-31	5.3360736243582115e-31

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	37
1	35	37
done	35	37

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	2586×	body	2560	valid
1.8s	2020×	body	10240	exit
1.7s	3407×	body	1280	valid
305.0ms	1098×	body	640	valid
163.0ms	10022×	pre	80	true
64.0ms	345×	body	320	valid
28.0ms	437×	body	80	valid
15.0ms	129×	body	160	valid