Details

sample90.0ms

Algorithm

intervals

Results

45.0ms

775×

body

valid

simplify8.6s

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	220	8
5	368	8
6	574	8
7	1186	8
8	3410	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
5.7b	(/ (* (cosh x) (/ y x)) z)

rewrite40.0ms

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×	`associate-l` `associate-/r*` `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 → 68

Calls

3 calls:

1.0ms	(cosh x)
16.0ms	(* (cosh x) (/ y x))
20.0ms	(/ (* (cosh x) (/ y x)) z)

series346.0ms

Counts

3 → 9

Calls

3 calls:

64.0ms	(cosh x)
120.0ms	(* (cosh x) (/ y x))
162.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.6s

Counts

77 → 77

Iterations

Useful iterations: 2 (322.0ms)

Iter	Nodes	Cost
0	150	773
1	355	735
2	1349	631
done	5001	631

prune235.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp x) (exp (- x)))
0.0b	(/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))
4.9b	(/ y (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
17×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt`
13×	`cbrt-undiv` `div-exp`
11×	`associate-/r/`
10×	`associate-*l/`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`flip3-+` `flip-+` `div-inv`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

3 → 87

Calls

3 calls:

17.0ms	(+ (exp x) (exp (- x)))
25.0ms	(/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))
43.0ms	(/ y (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))

series316.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(+ (exp x) (exp (- x)))
122.0ms	(/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))
165.0ms	(/ y (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: 2 (540.0ms)

Iter	Nodes	Cost
0	190	1958
1	500	1852
2	2314	1550
done	5000	1550

prune308.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ (exp x) (exp (- x))) 1/2) x)
0.0b	(+ (exp x) (exp (- x)))
0.2b	(/ z (/ (* (+ (exp x) (exp (- x))) 1/2) x))
4.9b	(/ y (/ z (/ (* (+ (exp x) (exp (- x))) 1/2) x)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
107×	`*-un-lft-identity`
105×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`associate-/r*`
32×	`add-exp-log` `add-cbrt-cube`
23×	`div-inv`
16×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
6×	`associate-/r/` `add-log-exp`
4×	`pow1`
3×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
2×	`flip3-+` `associate-*l/` `flip-+` `associate-/l/`
1×	`+-commutative` `sum-log` `distribute-lft-out`

Counts

4 → 209

Calls

4 calls:

49.0ms	(/ (* (+ (exp x) (exp (- x))) 1/2) x)
24.0ms	(+ (exp x) (exp (- x)))
37.0ms	(/ z (/ (* (+ (exp x) (exp (- x))) 1/2) x))
26.0ms	(/ y (/ z (/ (* (+ (exp x) (exp (- x))) 1/2) x)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (* (+ (exp x) (exp (- x))) 1/2) x)
37.0ms	(+ (exp x) (exp (- x)))
142.0ms	(/ z (/ (* (+ (exp x) (exp (- x))) 1/2) x))
212.0ms	(/ y (/ z (/ (* (+ (exp x) (exp (- x))) 1/2) x)))

simplify2.5s

Counts

221 → 221

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	388	4702
1	909	4462
2	3751	4136
done	5002	4130

prune924.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) y)
0.2b	(* (* (cosh x) y) (/ 1 x))
5.7b	(/ (* (* (cosh x) y) (/ 1 x)) z)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-exp-log`
36×	`add-cbrt-cube`
25×	`prod-exp`
17×	`add-sqr-sqrt` `div-exp`
16×	`associate-r`
15×	`add-cube-cbrt` `*-un-lft-identity`
13×	`cbrt-unprod`
12×	`times-frac`
11×	`pow1`
9×	`cbrt-undiv`
7×	`associate-*l/`
6×	`cosh-def`
4×	`rec-exp` `1-exp` `associate-l` `pow-prod-down` `associate-/l/` `add-log-exp`
3×	`associate-/r*`
2×	`frac-times` `associate-r/` `un-div-inv` `-commutative` `div-inv`
1×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

3.0ms	(cosh x)
16.0ms	(* (cosh x) y)
57.0ms	(* (* (cosh x) y) (/ 1 x))
50.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

series388.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(cosh x)
83.0ms	(* (cosh x) y)
99.0ms	(* (* (cosh x) y) (/ 1 x))
145.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

simplify1.6s

Counts

114 → 114

Iterations

Useful iterations: 2 (437.0ms)

Iter	Nodes	Cost
0	195	1280
1	487	1069
2	1781	857
done	5001	857

prune318.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes195.0ms

Accuracy

95.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 6.9b

bsearch154.0ms

Steps

Iters	Range		Point
9	1.86996669765208e-51	3.1713110469673597e-43	3.1233712431020393e-43
8	-1.2896703152085875e-21	-6.301225152323174e-25	-7.499151431129346e-22

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	22	50
1	28	37
done	28	37

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.7s

22060×

body

valid