Details

sample343.0ms

Algorithm

intervals

Results

19.0ms	39×	body	1280	valid
10.0ms	39×	body	640	valid
8.0ms	147×	body	80	valid
3.0ms	16×	body	320	valid
2.0ms	15×	body	160	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

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))

rewrite63.0ms

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)))
17.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
15.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- 1.0 (* (tan x) (tan x)))
97.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))
45.0ms	(* (tan x) (tan x))

simplify41.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (32.0ms)

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

prune243.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

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:

14.0ms	(* (tan x) (sin x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
30.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(* (tan x) (tan x))

series245.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (tan x) (sin x))
60.0ms	(/ (* (tan x) (sin x)) (cos x))
110.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
32.0ms	(* (tan x) (tan x))

simplify59.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (47.0ms)

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

prune311.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
26×	`times-frac`
21×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
7×	`associate-/l*`
6×	`pow1` `distribute-lft-out`
5×	`cbrt-undiv` `div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`associate-/l/` `add-log-exp`
3×	`tan-quot` `frac-2neg` `associate-r` `associate-l` `associate-*l/` `prod-exp` `clear-num` `cbrt-unprod` `div-inv`
2×	`associate-/r/`
1×	`flip3--` `flip3-+` `div-sub` `pow-prod-down` `*-commutative` `flip--` `flip-+` `unswap-sqr`

Counts

4 → 109

Calls

4 calls:

15.0ms	(* (tan x) (sin x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
41.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (tan x) (sin x))
58.0ms	(/ (* (tan x) (sin x)) (cos x))
61.0ms	(/ (* (tan x) (sin x)) (cos x))
127.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))

simplify50.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	393	1432
1	1572	1330
2	5001	1330

prune314.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
34×	`times-frac`
31×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
8×	`distribute-lft-out`
7×	`distribute-lft-out--`
6×	`associate-/r/` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv` `associate-/l*`
4×	`pow1` `difference-of-squares`
3×	`distribute-rgt-out--` `frac-2neg` `flip3-+` `clear-num` `flip-+`
2×	`tan-quot` `associate-*l/` `prod-exp` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 105

Calls

4 calls:

15.0ms	(/ (* (tan x) (sin x)) (cos x))
16.0ms	(/ (* (tan x) (sin x)) (cos x))
17.0ms	(/ 1.0 (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))
127.0ms	(- (/ 1.0 (+ 1.0 (/ (* (tan x) (sin x)) (cos x)))) (/ (/ (* (tan x) (sin x)) (cos x)) (+ 1.0 (/ (* (tan x) (sin x)) (cos x)))))

series406.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* (tan x) (sin x)) (cos x))
61.0ms	(/ (* (tan x) (sin x)) (cos x))
76.0ms	(/ 1.0 (+ 1.0 (/ (* (tan x) (sin x)) (cos x))))
212.0ms	(- (/ 1.0 (+ 1.0 (/ (* (tan x) (sin x)) (cos x)))) (/ (/ (* (tan x) (sin x)) (cos x)) (+ 1.0 (/ (* (tan x) (sin x)) (cos x)))))

simplify49.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	412	1595
1	1676	1497
2	5002	1497

prune312.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	13	20

end0.0ms

sample1.6s

Algorithm

intervals

Results

663.0ms	1505×	body	1280	valid
348.0ms	1244×	body	640	valid
246.0ms	4304×	body	80	valid
122.0ms	636×	body	320	valid
40.0ms	311×	body	160	valid