Details

sample80.0ms

Algorithm

intervals

Results

43.0ms

713×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2849
6	771
5	316
4	187
3	84
2	39
1	18
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
8.9b	(/ (* (cosh x) (/ y x)) z)

rewrite41.0ms

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:

18.0ms	(* (cosh x) (/ y x))
21.0ms	(/ (* (cosh x) (/ y x)) z)

series276.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (cosh x) (/ y x))
192.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
2	1331
1	352
0	141

prune500.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(* (+ (exp x) (exp (- x))) y)
6.6b	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

19.0ms	(+ (exp x) (exp (- x)))
72.0ms	(* (+ (exp x) (exp (- x))) y)
50.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

series271.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+ (exp x) (exp (- x)))
100.0ms	(* (+ (exp x) (exp (- x))) y)
144.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

simplify1.6s

Counts

78 → 78

Iterations

Iter	Nodes
done	5006
2	2151
1	426
0	144

prune443.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

0.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
4.0ms	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
5.0ms	(/ 1/2 (exp x))
24.0ms	(* (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x) (/ y z))

series316.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
88.0ms	(/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x)
18.0ms	(/ 1/2 (exp x))
162.0ms	(* (/ (fma (exp x) 1/2 (/ 1/2 (exp x))) x) (/ y z))

simplify1.7s

Counts

132 → 132

Iterations

Iter	Nodes
done	5000
2	1752
1	537
0	213

prune737.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt z)
0.5b	(cbrt z)
0.5b	(* (cbrt z) (cbrt z))
5.2b	(* (/ (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) x) (* (cbrt z) (cbrt z))) (/ y (cbrt z)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
55×	`times-frac`
47×	`add-exp-log`
35×	`*-un-lft-identity` `add-cube-cbrt`
34×	`cbrt-prod`
32×	`add-cbrt-cube`
28×	`associate-r`
23×	`associate-l`
17×	`cbrt-undiv` `div-exp`
15×	`prod-exp` `cbrt-unprod`
13×	`pow1` `unswap-sqr`
8×	`pow1/3`
6×	`swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `associate-r/`

Counts

4 → 150

Calls

4 calls:

1.0ms	(cbrt z)
1.0ms	(cbrt z)
12.0ms	(* (cbrt z) (cbrt z))
66.0ms	(* (/ (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) x) (* (cbrt z) (cbrt z))) (/ y (cbrt z)))

series991.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt z)
250.0ms	(cbrt z)
294.0ms	(* (cbrt z) (cbrt z))
203.0ms	(* (/ (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) x) (* (cbrt z) (cbrt z))) (/ y (cbrt z)))

simplify2.4s

Counts

162 → 162

Iterations

Iter	Nodes
done	5010
2	3786
1	748
0	248

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes696.0ms

Accuracy

92.5% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 6.2b

bsearch137.0ms

Steps

Iters	Range		Point
7	7.116247436874675e-60	1.773079517275612e-58	1.7439336583180414e-58
7	-1.977625587217465e-41	-2.706067999623793e-43	-2.2836121162778763e-42

simplify11.0ms

Iterations

Iter	Nodes
done	38
1	38
0	30

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.5s

22614×

body

valid