Details

sample80.0ms

Algorithm

intervals

Results

42.0ms

671×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1941
5	509
4	226
3	102
2	41
1	18
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.8b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cosh x) (/ y x))
7.1b	(/ (* (cosh x) (/ y x)) z)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 64

Calls

2 calls:

12.0ms	(* (cosh x) (/ y x))
15.0ms	(/ (* (cosh x) (/ y x)) z)

series274.0ms

Counts

2 → 6

Calls

2 calls:

108.0ms	(* (cosh x) (/ y x))
167.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.3s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1549
1	354
0	141

prune351.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (cosh x) y) (/ 1 x))
0.2b	(* (cosh x) y)
7.1b	(/ (* (* (cosh x) y) (/ 1 x)) z)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 100

Calls

3 calls:

20.0ms	(* (* (cosh x) y) (/ 1 x))
6.0ms	(* (cosh x) y)
21.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

series407.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(* (* (cosh x) y) (/ 1 x))
114.0ms	(* (cosh x) y)
186.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

simplify3.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	3541
1	548
0	190

prune533.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/2 (exp x) (/ 1/2 (exp x)))
0.0b	(/ 1/2 (exp x))
0.2b	(* (/ y x) (fma 1/2 (exp x) (/ 1/2 (exp x))))
7.1b	(/ (* (/ y x) (fma 1/2 (exp x) (/ 1/2 (exp x)))) z)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-l`
6×	`pow1` `cbrt-undiv` `associate-/r*` `div-exp`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-r` `fma-udef` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 101

Calls

4 calls:

0.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
5.0ms	(/ 1/2 (exp x))
12.0ms	(* (/ y x) (fma 1/2 (exp x) (/ 1/2 (exp x))))
11.0ms	(/ (* (/ y x) (fma 1/2 (exp x) (/ 1/2 (exp x)))) z)

series380.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
19.0ms	(/ 1/2 (exp x))
124.0ms	(* (/ y x) (fma 1/2 (exp x) (/ 1/2 (exp x))))
162.0ms	(/ (* (/ y x) (fma 1/2 (exp x) (/ 1/2 (exp x)))) z)

simplify2.2s

Counts

113 → 113

Iterations

Iter	Nodes
done	5001
2	3010
1	452
0	190

prune724.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (cosh x) y) (/ 1 x))
0.2b	(* (cosh x) y)
7.1b	(* (* (* (cosh x) y) (/ 1 x)) (/ 1 z))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-exp-log`
97×	`prod-exp`
58×	`add-cbrt-cube`
38×	`div-exp`
29×	`associate-r` `cbrt-unprod`
21×	`add-sqr-sqrt`
19×	`pow1` `rec-exp` `*-un-lft-identity` `1-exp` `add-cube-cbrt`
18×	`times-frac`
14×	`associate-*l/`
11×	`cbrt-undiv`
10×	`pow-prod-down`
7×	`frac-times` `cosh-def`
5×	`associate-l`
4×	`associate-*r/` `un-div-inv`
3×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`div-inv`
1×	`unswap-sqr`

Counts

3 → 146

Calls

3 calls:

42.0ms	(* (* (cosh x) y) (/ 1 x))
12.0ms	(* (cosh x) y)
100.0ms	(* (* (* (cosh x) y) (/ 1 x)) (/ 1 z))

series445.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(* (* (cosh x) y) (/ 1 x))
129.0ms	(* (cosh x) y)
188.0ms	(* (* (* (cosh x) y) (/ 1 x)) (/ 1 z))

simplify1.0s

Counts

155 → 155

Iterations

Iter	Nodes
done	5000
1	805
0	244

prune633.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.2b

regimes432.0ms

Accuracy

95.7% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 6.7b

bsearch177.0ms

Steps

Iters	Range		Point
9	703048693117.0839	2.4011621868508918e+17	1431949075770.4272
10	-6.4954074094430426e-40	-2.925517781079411e-51	-6.427833610272478e-40

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.9s

22383×

body

valid