Details

sample97.0ms

Algorithm

intervals

Results

49.0ms

775×

body

valid

simplify8.7s

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	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

localize16.0ms

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)

rewrite52.0ms

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)
20.0ms	(* (cosh x) (/ y x))
28.0ms	(/ (* (cosh x) (/ y x)) z)

series390.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(cosh x)
133.0ms	(* (cosh x) (/ y x))
196.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.7s

Counts

77 → 77

Iterations

Useful iterations: 2 (323.0ms)

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

prune273.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

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)))

rewrite83.0ms

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:

21.0ms	(+ (exp x) (exp (- x)))
28.0ms	(/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))
27.0ms	(/ y (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))

series462.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (exp x) (exp (- x)))
190.0ms	(/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))
230.0ms	(/ y (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))

simplify1.3s

Counts

96 → 96

Iterations

Useful iterations: 2 (524.0ms)

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

prune409.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize10.0ms

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)

rewrite99.0ms

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:

1.0ms	(cosh x)
8.0ms	(* (cosh x) y)
37.0ms	(* (* (cosh x) y) (/ 1 x))
48.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

series444.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(cosh x)
98.0ms	(* (cosh x) y)
100.0ms	(* (* (cosh x) y) (/ 1 x))
165.0ms	(/ (* (* (cosh x) y) (/ 1 x)) z)

simplify1.7s

Counts

114 → 114

Iterations

Useful iterations: 2 (494.0ms)

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

prune296.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
1.7b	(/ (cbrt y) (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))
3.6b	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
78×	`add-exp-log`
55×	`add-sqr-sqrt`
52×	`cbrt-prod`
51×	`add-cbrt-cube`
50×	`add-cube-cbrt` `*-un-lft-identity`
47×	`associate-r`
30×	`prod-exp` `cbrt-unprod`
28×	`associate-/r/`
27×	`cbrt-undiv` `div-exp`
26×	`associate-*l/`
15×	`div-inv`
13×	`flip3-+` `flip-+`
9×	`pow1`
7×	`associate-/r*`
6×	`associate-/l*`
4×	`add-log-exp`
3×	`pow-prod-down` `unswap-sqr`
2×	`pow1/3`
1×	`frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 184

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
34.0ms	(/ (cbrt y) (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))
155.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

261.0ms	(cbrt y)
275.0ms	(cbrt y)
292.0ms	(/ (cbrt y) (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2)))
251.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (/ (* z x) (* (+ (exp x) (exp (- x))) 1/2))))

simplify2.6s

Counts

196 → 196

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	297	4635
1	866	4405
2	4346	3572
done	5000	3432

prune843.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes171.0ms

Accuracy

95.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 6.9b

bsearch203.0ms

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

sample3.1s

Algorithm

intervals

Results

1.5s

22060×

body

valid