Details

sample78.0ms

Algorithm

intervals

Results

46.0ms

668×

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
6.9b	(/ (* (cosh x) (/ y x)) z)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

1.0ms	(cosh x)
13.0ms	(* (cosh x) (/ y x))
13.0ms	(/ (* (cosh x) (/ y x)) z)

series311.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(cosh x)
98.0ms	(* (cosh x) (/ y x))
157.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.2s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
2	1438
1	386
0	156

prune529.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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))) (/ y z))
0.0b	(/ 1/2 (exp x))
4.8b	(/ (* (fma (exp x) 1/2 (/ 1/2 (exp x))) (/ y z)) x)

rewrite44.0ms

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-r`
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-l` `div-inv`
2×	`clear-num` `frac-2neg` `associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 99

Calls

4 calls:

0.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
18.0ms	(* (fma (exp x) 1/2 (/ 1/2 (exp x))) (/ y z))
9.0ms	(/ 1/2 (exp x))
13.0ms	(/ (* (fma (exp x) 1/2 (/ 1/2 (exp x))) (/ y z)) x)

series353.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(fma (exp x) 1/2 (/ 1/2 (exp x)))
117.0ms	(* (fma (exp x) 1/2 (/ 1/2 (exp x))) (/ y z))
17.0ms	(/ 1/2 (exp x))
178.0ms	(/ (* (fma (exp x) 1/2 (/ 1/2 (exp x))) (/ y z)) x)

simplify1.6s

Counts

111 → 111

Iterations

Iter	Nodes
done	5000
2	1436
1	445
0	190

prune723.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
0.0b	(/ 1/2 (exp x))
0.2b	(* (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) y)
4.8b	(/ (* (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) y) x)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
31×	`times-frac`
30×	`*-un-lft-identity` `add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`add-exp-log`
13×	`associate-l`
9×	`associate-/r*`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`associate-*l/` `unswap-sqr`
1×	`pow-prod-down` `*-commutative` `associate-/l/`

Counts

4 → 118

Calls

4 calls:

4.0ms	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
5.0ms	(/ 1/2 (exp x))
12.0ms	(* (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) y)
12.0ms	(/ (* (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) y) x)

series370.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
18.0ms	(/ 1/2 (exp x))
120.0ms	(* (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) y)
140.0ms	(/ (* (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) y) x)

simplify2.2s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1670
1	470
0	208

prune907.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/2 (exp x) (/ 1/2 (exp x)))
0.0b	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
0.0b	(/ 1/2 (exp x))
6.6b	(/ (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) (/ x y))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

439×	`times-frac`
216×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
31×	`div-inv`
20×	`add-cbrt-cube`
19×	`associate-/r` `add-exp-log` `associate-/l`
10×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`associate-/r/` `fma-udef` `associate-/l/`

Counts

4 → 285

Calls

4 calls:

1.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
8.0ms	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
10.0ms	(/ 1/2 (exp x))
29.0ms	(/ (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) (/ x y))

series385.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(fma 1/2 (exp x) (/ 1/2 (exp x)))
117.0ms	(/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z)
19.0ms	(/ 1/2 (exp x))
171.0ms	(/ (/ (fma 1/2 (exp x) (/ 1/2 (exp x))) z) (/ x y))

simplify2.0s

Counts

297 → 297

Iterations

Iter	Nodes
done	5000
1	1540
0	524

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

regimes235.0ms

Accuracy

93.7% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 6.9b

bsearch170.0ms

Steps

Iters	Range		Point
8	2.2109201577283574e+46	1.7322668861585903e+49	2.2322067363708056e+46
10	-9.52971775302429e-34	-1.0556828637573711e-50	-9.31808310867496e-34

simplify4.0ms

Iterations

Iter	Nodes
done	34
1	34
0	23

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.4s

22172×

body

valid