Details

sample92.0ms

Algorithm

intervals

Results

55.0ms

793×

body

valid

simplify8.1s

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	224	8
5	377	8
6	592	8
7	1228	8
8	3476	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.3b	(* (cosh x) (/ y x))
8.2b	(/ (* (cosh x) (/ y x)) z)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

1.0ms	(cosh x)
15.0ms	(* (cosh x) (/ y x))
24.0ms	(/ (* (cosh x) (/ y x)) z)

series366.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(cosh x)
130.0ms	(* (cosh x) (/ y x))
174.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.5s

Counts

83 → 83

Iterations

Useful iterations: 2 (347.0ms)

Iter	Nodes	Cost
0	156	811
1	366	770
2	1353	665
done	5000	665

prune313.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.2b	(* (+ (exp x) (exp (- x))) y)
4.4b	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 69

Calls

3 calls:

13.0ms	(+ (exp x) (exp (- x)))
61.0ms	(* (+ (exp x) (exp (- x))) y)
33.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

series251.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (exp x) (exp (- x)))
73.0ms	(* (+ (exp x) (exp (- x))) y)
140.0ms	(/ (* (+ (exp x) (exp (- x))) y) (* z (* 2 x)))

simplify1.3s

Counts

78 → 78

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	145	1158
1	410	1102
2	2014	863
done	5000	854

prune209.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp (- x)) 3)
0.2b	(/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x))))
0.2b	(* (/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x)))) y)
4.4b	(/ (* (/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x)))) y) (* z (* 2 x)))

rewrite319.0ms

Algorithm

rewrite-expression-head

Rules

108×	`*-un-lft-identity`
56×	`times-frac`
48×	`add-cbrt-cube`
47×	`add-exp-log`
43×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
35×	`distribute-lft-out`
31×	`unpow-prod-down` `cube-prod` `associate-l`
17×	`prod-exp` `cbrt-unprod`
14×	`cbrt-undiv` `div-exp`
11×	`pow-pow`
10×	`exp-prod` `associate-/l*`
7×	`pow1` `sum-cubes`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`distribute-lft-neg-in` `pow-unpow` `distribute-rgt-neg-in` `associate-r` `div-inv` `associate-/l/`
2×	`cube-div` `frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`neg-sub0` `exp-neg` `cube-mult` `pow-to-exp` `neg-mul-1` `flip3-+` `exp-diff` `unpow3` `pow-prod-down` `pow-exp` `*-commutative` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 178

Calls

4 calls:

9.0ms	(pow (exp (- x)) 3)
99.0ms	(/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x))))
135.0ms	(* (/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x)))) y)
67.0ms	(/ (* (/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x)))) y) (* z (* 2 x)))

series900.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (exp (- x)) 3)
204.0ms	(/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x))))
291.0ms	(* (/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x)))) y)
362.0ms	(/ (* (/ (+ (pow (exp x) 3) (pow (exp (- x)) 3)) (fma (exp x) (exp x) (expm1 (* -2 x)))) y) (* z (* 2 x)))

simplify1.9s

Counts

190 → 190

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	277	5136
1	703	4951
2	3021	4128
done	5001	3979

prune812.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp (- x)) 3)
0.7b	(* (/ (sqrt (+ (pow (exp x) 3) (pow (exp (- x)) 3))) 1) (/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y)))
0.7b	(/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y))
4.4b	(/ (* (/ (sqrt (+ (pow (exp x) 3) (pow (exp (- x)) 3))) 1) (/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y))) (* z (* 2 x)))

rewrite425.0ms

Algorithm

rewrite-expression-head

Rules

205×	`times-frac`
192×	`add-exp-log`
157×	`add-sqr-sqrt`
142×	`*-un-lft-identity`
139×	`add-cbrt-cube`
106×	`add-cube-cbrt`
93×	`div-exp`
66×	`prod-exp`
60×	`cbrt-undiv`
45×	`cbrt-unprod`
44×	`associate-r`
40×	`associate-l`
33×	`sqrt-prod`
15×	`unpow-prod-down` `cube-prod` `distribute-lft-out` `unswap-sqr`
14×	`associate-/r*`
12×	`1-exp`
11×	`pow-pow` `div-inv`
10×	`exp-prod`
7×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`distribute-lft-neg-in` `pow-unpow` `distribute-rgt-neg-in` `sum-cubes` `associate-/l/`
2×	`cube-div` `frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r/`
1×	`neg-sub0` `exp-neg` `cube-mult` `pow-to-exp` `neg-mul-1` `exp-diff` `unpow3` `pow-prod-down` `pow-exp` `*-commutative` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 306

Calls

4 calls:

10.0ms	(pow (exp (- x)) 3)
292.0ms	(* (/ (sqrt (+ (pow (exp x) 3) (pow (exp (- x)) 3))) 1) (/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y)))
17.0ms	(/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y))
88.0ms	(/ (* (/ (sqrt (+ (pow (exp x) 3) (pow (exp (- x)) 3))) 1) (/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y))) (* z (* 2 x)))

series2.2s

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (exp (- x)) 3)
726.0ms	(* (/ (sqrt (+ (pow (exp x) 3) (pow (exp (- x)) 3))) 1) (/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y)))
544.0ms	(/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y))
931.0ms	(/ (* (/ (sqrt (+ (pow (exp x) 3) (pow (exp (- x)) 3))) 1) (/ (hypot (pow (exp x) 3/2) (pow (exp (- x)) 3/2)) (/ (fma (exp x) (exp x) (expm1 (* -2 x))) y))) (* z (* 2 x)))

simplify3.7s

Counts

318 → 318

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	512	14271
1	1285	12952
2	4928	9418
done	5000	9416

prune2.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.2b

regimes242.0ms

Accuracy

95% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.3b

bsearch171.0ms

Steps

Iters	Range		Point
9	17022.421552551856	814748756446.3522	189132.75325345353
9	-8.486168864013548e+42	-3.5012581466619693e+37	-7.575455656273212e+37

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	30	78
1	40	51
done	40	51

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s

22231×

body

valid