Details

sample357.0ms

Algorithm

intervals

Results

22.0ms	51×	body	1280	valid
11.0ms	41×	body	640	valid
9.0ms	133×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid

simplify13.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	21	9
2	26	9
3	34	9
4	37	9
5	37	9
done	37	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

10.0ms	(- 1.0 (* (tan x) (tan x)))
18.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series214.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- 1.0 (* (tan x) (tan x)))
100.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
33.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify42.0ms

Counts

117 → 117

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	314	909
1	1157	838
2	5001	824
done	5001	824

prune239.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(* (tan x) (sin x))
0.3b	(* (tan x) (tan x))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
13×	`pow1`
6×	`tan-quot` `associate-r` `associate-l` `associate-/r` `associate-/l`
4×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`cbrt-undiv` `swap-sqr` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `frac-times` `flip3--` `flip3-+` `pow-plus` `div-sub` `associate-*r/` `pow-sqr` `pow-prod-up` `flip--` `flip-+`

Counts

4 → 109

Calls

4 calls:

17.0ms	(/ (* (tan x) (sin x)) (cos x))
31.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
13.0ms	(* (tan x) (sin x))
17.0ms	(* (tan x) (tan x))

series253.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (* (tan x) (sin x)) (cos x))
113.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
46.0ms	(* (tan x) (sin x))
34.0ms	(* (tan x) (tan x))

simplify57.0ms

Counts

121 → 121

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	441	1158
1	1849	1060
2	5001	1054
done	5001	1054

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (sin x))
0.2b	(exp (* (tan x) (sin x)))
0.3b	(* (tan x) (tan x))
2.2b	(log (exp (* (tan x) (sin x))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`pow1`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`associate-r` `associate-l`
5×	`tan-quot`
3×	`log-prod` `swap-sqr` `log-pow`
2×	`exp-prod` `exp-to-pow` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `frac-times` `pow-plus` `associate-*r/` `rem-log-exp` `pow-sqr` `pow-prod-up` `rem-exp-log`

Counts

4 → 71

Calls

4 calls:

13.0ms	(* (tan x) (sin x))
13.0ms	(exp (* (tan x) (sin x)))
15.0ms	(* (tan x) (tan x))
4.0ms	(log (exp (* (tan x) (sin x))))

series182.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan x) (sin x))
57.0ms	(exp (* (tan x) (sin x)))
35.0ms	(* (tan x) (tan x))
44.0ms	(log (exp (* (tan x) (sin x))))

simplify102.0ms

Counts

83 → 83

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	181	388
1	614	335
2	3185	326
3	5002	323
done	5002	323

prune238.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))
0.3b	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
30×	`add-cube-cbrt` `*-un-lft-identity`
24×	`times-frac`
19×	`pow1` `log-pow`
18×	`exp-prod`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
7×	`difference-of-squares`
6×	`swap-sqr` `associate-r` `associate-l`
4×	`associate-/r/` `associate-/l*` `add-log-exp`
3×	`log-prod` `associate-/r*`
2×	`pow2` `frac-times` `flip3-+` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `div-inv` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip--`

Counts

4 → 123

Calls

4 calls:

17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))
15.0ms	(* (tan x) (tan x))
26.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
35.0ms	(* (tan x) (tan x))
98.0ms	(log (exp (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))

simplify41.0ms

Counts

135 → 135

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	362	1207
1	1191	1116
2	5001	1100
done	5001	1100

prune303.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	13
1	15	13
done	15	13

end0.0ms

sample1.6s

Algorithm

intervals

Results

690.0ms	1545×	body	1280	valid
324.0ms	1180×	body	640	valid
252.0ms	4370×	body	80	valid
116.0ms	585×	body	320	valid
42.0ms	320×	body	160	valid