Details

sample99.0ms

Algorithm

intervals

Results

56.0ms

704×

body

valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	18	8
2	41	8
3	102	8
4	226	8
5	508	8
6	1898	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
6.5b	(/ (* (cosh x) (/ y x)) z)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`add-exp-log` `add-cbrt-cube`
13×	`times-frac` `associate-r`
12×	`add-cube-cbrt` `*-un-lft-identity`
5×	`cbrt-undiv` `div-exp`
4×	`pow1` `cosh-def` `prod-exp` `cbrt-unprod`
3×	`associate-l` `associate-/r*` `associate-/l/`
2×	`expm1-log1p-u` `frac-times` `associate-r/` `associate-l/` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `-commutative` `associate-/l`

Counts

2 → 64

Calls

2 calls:

15.0ms	(* (cosh x) (/ y x))
21.0ms	(/ (* (cosh x) (/ y x)) z)

series267.0ms

Counts

2 → 6

Calls

2 calls:

116.0ms	(* (cosh x) (/ y x))
151.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.5s

Counts

70 → 70

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	141	739
1	354	701
2	1584	606
done	5000	600

prune227.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (- x)) (exp x))
0.3b	(/ (* 1/2 (+ (exp (- x)) (exp x))) (/ x y))
6.5b	(/ (/ (* 1/2 (+ (exp (- x)) (exp x))) (/ x y)) z)

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

173×	`times-frac`
71×	`*-un-lft-identity`
69×	`add-sqr-sqrt` `add-cube-cbrt`
33×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/l*`
17×	`cbrt-undiv` `div-exp`
16×	`associate-/r*`
12×	`div-inv`
5×	`associate-/r/` `add-log-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `expm1-log1p-u` `fma-def` `log1p-expm1-u` `associate-/l/`
2×	`frac-2neg` `flip3-+` `associate-*r/` `clear-num` `flip-+`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

3 → 165

Calls

3 calls:

31.0ms	(+ (exp (- x)) (exp x))
69.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) (/ x y))
76.0ms	(/ (/ (* 1/2 (+ (exp (- x)) (exp x))) (/ x y)) z)

series301.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(+ (exp (- x)) (exp x))
101.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) (/ x y))
157.0ms	(/ (/ (* 1/2 (+ (exp (- x)) (exp x))) (/ x y)) z)

simplify700.0ms

Counts

174 → 174

Iterations

Useful iterations: done (692.0ms)

Iter	Nodes	Cost
0	330	3307
1	962	3145
done	5001	2867

prune884.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
1.3b	(/ (/ 1/2 (/ (* (cbrt x) (cbrt x)) (* (cbrt y) (cbrt y)))) (* (cbrt z) (cbrt z)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
56×	`times-frac`
32×	`add-cbrt-cube`
30×	`cbrt-undiv` `div-exp`
25×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
20×	`associate-/l*`
14×	`prod-exp` `cbrt-unprod`
9×	`cbrt-prod` `div-inv`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`associate-/r/`
1×	`frac-2neg` `clear-num` `associate-/r*` `associate-/l/`

Counts

4 → 117

Calls

4 calls:

2.0ms	(cbrt x)
2.0ms	(cbrt x)
2.0ms	(cbrt x)
65.0ms	(/ (/ 1/2 (/ (* (cbrt x) (cbrt x)) (* (cbrt y) (cbrt y)))) (* (cbrt z) (cbrt z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt x)
330.0ms	(cbrt x)
277.0ms	(cbrt x)
228.0ms	(/ (/ 1/2 (/ (* (cbrt x) (cbrt x)) (* (cbrt y) (cbrt y)))) (* (cbrt z) (cbrt z)))

simplify1.8s

Counts

129 → 129

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	253	2373
1	725	2257
2	3521	1790
done	5000	1671

prune827.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (- x)) (exp x))
0.0b	(/ (* 1/2 (+ (exp (- x)) (exp x))) x)
5.0b	(* (/ (* 1/2 (+ (exp (- x)) (exp x))) x) (/ y z))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`times-frac`
15×	`add-cube-cbrt`
13×	`associate-r`
9×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
7×	`associate-l`
5×	`pow1` `add-log-exp`
3×	`expm1-log1p-u` `fma-def` `associate-r/` `associate-/r` `log1p-expm1-u` `div-inv`
2×	`flip3-+` `flip-+` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `distribute-lft-out` `associate-/l*`

Counts

3 → 90

Calls

3 calls:

38.0ms	(+ (exp (- x)) (exp x))
41.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) x)
142.0ms	(* (/ (* 1/2 (+ (exp (- x)) (exp x))) x) (/ y z))

series255.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(+ (exp (- x)) (exp x))
104.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) x)
119.0ms	(* (/ (* 1/2 (+ (exp (- x)) (exp x))) x) (/ y z))

simplify3.0s

Counts

99 → 99

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	188	1583
1	589	1495
2	4112	1257
done	5001	1253

prune385.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes196.0ms

Accuracy

88.1% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 2.8b

bsearch173.0ms

Steps

Iters	Range		Point
9	1.2937792643658544e+50	6.441435588545496e+55	1.345654323883122e+50
8	-7.151692826123706e-13	-5.243712960536707e-17	-1.7065242675146888e-14

simplify7.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	50
1	29	37
done	29	37

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.7s

22397×

body

valid