Details

sample79.0ms

Algorithm

intervals

Results

37.0ms

775×

body

valid

simplify7.4s

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.1b

localize11.0ms

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)

rewrite38.0ms

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

series262.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(cosh x)
87.0ms	(* (cosh x) (/ y x))
124.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.5s

Counts

83 → 83

Iterations

Useful iterations: 2 (296.0ms)

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

prune223.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) y)
4.9b	(/ (* (cosh x) y) (* x z))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 55

Calls

3 calls:

2.0ms	(cosh x)
12.0ms	(* (cosh x) y)
15.0ms	(/ (* (cosh x) y) (* x z))

series317.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(cosh x)
85.0ms	(* (cosh x) y)
154.0ms	(/ (* (cosh x) y) (* x z))

simplify989.0ms

Counts

64 → 64

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	119	584
1	296	562
2	1276	462
done	5001	462

prune188.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.4b	(cbrt (/ (* (cosh x) y) (* x z)))
4.9b	(/ (* (cosh x) y) (* x z))
4.9b	(/ (* (cosh x) y) (* x z))
4.9b	(/ (* (cosh x) y) (* x z))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

6.0ms	(cbrt (/ (* (cosh x) y) (* x z)))
18.0ms	(/ (* (cosh x) y) (* x z))
14.0ms	(/ (* (cosh x) y) (* x z))
19.0ms	(/ (* (cosh x) y) (* x z))

series672.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(cbrt (/ (* (cosh x) y) (* x z)))
174.0ms	(/ (* (cosh x) y) (* x z))
143.0ms	(/ (* (cosh x) y) (* x z))
125.0ms	(/ (* (cosh x) y) (* x z))

simplify843.0ms

Counts

100 → 100

Iterations

Useful iterations: done (840.0ms)

Iter	Nodes	Cost
0	131	1342
1	318	1288
2	1290	1018
done	5000	1011

prune274.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cosh x) y))
0.6b	(cbrt (* (cosh x) y))
0.6b	(cbrt (* (cosh x) y))
4.9b	(/ (* (* (cbrt (* (cosh x) y)) (cbrt (* (cosh x) y))) (cbrt (* (cosh x) y))) (* x z))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
20×	`associate-*l/`
17×	`add-cbrt-cube`
15×	`cbrt-div` `cosh-def`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-/l/`
6×	`cbrt-undiv` `div-exp`
5×	`frac-times`
4×	`pow1` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `associate-*r/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 70

Calls

4 calls:

7.0ms	(cbrt (* (cosh x) y))
6.0ms	(cbrt (* (cosh x) y))
6.0ms	(cbrt (* (cosh x) y))
87.0ms	(/ (* (* (cbrt (* (cosh x) y)) (cbrt (* (cosh x) y))) (cbrt (* (cosh x) y))) (* x z))

series757.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(cbrt (* (cosh x) y))
179.0ms	(cbrt (* (cosh x) y))
180.0ms	(cbrt (* (cosh x) y))
215.0ms	(/ (* (* (cbrt (* (cosh x) y)) (cbrt (* (cosh x) y))) (cbrt (* (cosh x) y))) (* x z))

simplify1.5s

Counts

82 → 82

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	128	1313
1	335	1263
2	1473	820
done	5001	704

prune281.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes244.0ms

Accuracy

95.2% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.0b

bsearch118.0ms

Steps

Iters	Range		Point
9	4.861077116233833e+20	6.6094121709703044e+25	1.8049362431750824e+23
7	-3.423602116682063e-37	-4.786244883458866e-39	-3.3781132449665854e-37

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	16	32
1	22	25
done	22	25

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s

22060×

body

valid