Details

sample54.0ms

Algorithm

intervals

Results

26.0ms

749×

body

valid

simplify1.7s

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	222	8
5	500	8
6	1889	8
done	5000	8

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.5b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (cosh x) (/ y x))
7.9b	(/ (* (cosh x) (/ y x)) z)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 60

Calls

2 calls:

25.0ms	(* (cosh x) (/ y x))
26.0ms	(/ (* (cosh x) (/ y x)) z)

series264.0ms

Counts

2 → 6

Calls

2 calls:

110.0ms	(* (cosh x) (/ y x))
153.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.3s

Counts

66 → 66

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	137	707
1	347	670
2	1562	584
done	5001	570

prune225.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (- x)) (exp x))
0.4b	(/ (* 1/2 (+ (exp (- x)) (exp x))) (/ (* z x) y))
6.4b	(/ (* z x) y)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

20.0ms	(+ (exp (- x)) (exp x))
43.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) (/ (* z x) y))
11.0ms	(/ (* z x) y)

series234.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(+ (exp (- x)) (exp x))
169.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) (/ (* z x) y))
32.0ms	(/ (* z x) y)

simplify1.7s

Counts

82 → 82

Iterations

Useful iterations: 2 (524.0ms)

Iter	Nodes	Cost
0	157	1233
1	501	1177
2	3221	967
done	5000	967

prune348.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (- x)) (exp x))
0.3b	(/ (* 1/2 (+ (exp (- x)) (exp x))) (* z x))
6.9b	(* (/ (* 1/2 (+ (exp (- x)) (exp x))) (* z x)) y)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log` `add-cbrt-cube`
13×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-cube-cbrt` `associate-l` `add-log-exp`
3×	`associate-r`
2×	`flip3-+` `times-frac` `associate-*r/` `flip-+` `div-inv` `associate-/l/`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `sum-log` `-commutative` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 64

Calls

3 calls:

19.0ms	(+ (exp (- x)) (exp x))
32.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) (* z x))
90.0ms	(* (/ (* 1/2 (+ (exp (- x)) (exp x))) (* z x)) y)

series222.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (exp (- x)) (exp x))
76.0ms	(/ (* 1/2 (+ (exp (- x)) (exp x))) (* z x))
121.0ms	(* (/ (* 1/2 (+ (exp (- x)) (exp x))) (* z x)) y)

simplify1.6s

Counts

73 → 73

Iterations

Useful iterations: 2 (496.0ms)

Iter	Nodes	Cost
0	151	1306
1	468	1240
2	3590	950
done	5000	950

prune257.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (exp (- x)) (exp x))
0.0b	(* (* 1/2 (+ (exp (- x)) (exp x))) (/ y (* x z)))
6.5b	(/ y (* x z))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-exp-log` `add-cbrt-cube`
12×	`prod-exp` `cbrt-unprod`
9×	`*-un-lft-identity`
8×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt` `associate-r`
6×	`cbrt-undiv` `times-frac` `div-exp`
5×	`associate-*r/` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `flip-+` `associate-/l*`
2×	`frac-times` `associate-*l/` `div-inv`
1×	`+-commutative` `frac-2neg` `associate-l` `clear-num` `associate-/r` `sum-log` `-commutative` `distribute-lft-out`

Counts

3 → 68

Calls

3 calls:

27.0ms	(+ (exp (- x)) (exp x))
129.0ms	(* (* 1/2 (+ (exp (- x)) (exp x))) (/ y (* x z)))
8.0ms	(/ y (* x z))

series207.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+ (exp (- x)) (exp x))
138.0ms	(* (* 1/2 (+ (exp (- x)) (exp x))) (/ y (* x z)))
31.0ms	(/ y (* x z))

simplify1.7s

Counts

77 → 77

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	145	1159
1	447	1100
2	2999	886
done	5000	881

prune262.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes157.0ms

Accuracy

88.4% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 7.0b

bsearch125.0ms

Steps

Iters	Range		Point
8	2.0961804712629655e-72	1.9571072620604557e-68	1.9092807616058557e-68
6	-7.141856567206707e+81	-9.593165182687808e+80	-9.805921840000082e+80

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	21	50
1	28	37
done	28	37

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s

22555×

body

valid