Details

sample362.0ms

Algorithm

intervals

Results

19.0ms	39×	body	1280	valid
11.0ms	39×	body	640	valid
9.0ms	147×	body	80	valid
3.0ms	16×	body	320	valid
2.0ms	15×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	13	9
1	22	9
2	29	9
3	37	9
4	43	9
5	45	9
6	45	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

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))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`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×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg` `prod-diff` `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 → 119

Calls

4 calls:

11.0ms	(- 1.0 (* (tan x) (tan x)))
19.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
17.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series215.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- 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))
44.0ms	(* (tan x) (tan x))

simplify44.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	917
2	5001	882

prune283.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
0.2b	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1`
16×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

4 → 82

Calls

4 calls:

0.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
14.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

series581.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(expm1 (log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))))
222.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
35.0ms	(* (tan x) (tan x))
33.0ms	(* (tan x) (tan x))

simplify96.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	204	664
1	683	574
2	2965	552
3	5001	546

prune219.0ms

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))

rewrite86.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 117

Calls

4 calls:

15.0ms	(* (tan x) (sin x))
15.0ms	(/ (* (tan x) (sin x)) (cos x))
35.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
18.0ms	(* (tan x) (tan x))

series256.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (tan x) (sin x))
63.0ms	(/ (* (tan x) (sin x)) (cos x))
117.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
34.0ms	(* (tan x) (tan x))

simplify63.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	455	1207
1	1904	1097
2	5001	1088

prune339.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
0.3b	(* (tan x) (tan x))
13.2b	(sqrt (/ (* (tan x) (sin x)) (cos x)))
13.2b	(sqrt (/ (* (tan x) (sin x)) (cos x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

48×	`sqrt-prod`
40×	`add-sqr-sqrt`
28×	`pow1`
24×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`swap-sqr`
13×	`associate-r` `associate-l`
10×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `add-cbrt-cube`
6×	`sqrt-div` `pow-prod-up` `div-inv`
5×	`unswap-sqr`
4×	`tan-quot` `expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`sqrt-unprod` `rem-square-sqrt`

Counts

4 → 136

Calls

4 calls:

40.0ms	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
15.0ms	(* (tan x) (tan x))
5.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
6.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (sqrt (/ (* (tan x) (sin x)) (cos x))) (sqrt (/ (* (tan x) (sin x)) (cos x))))
32.0ms	(* (tan x) (tan x))
78.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))
83.0ms	(sqrt (/ (* (tan x) (sin x)) (cos x)))

simplify50.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	252	1113
1	1134	996
2	5002	950

prune376.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes129.0ms

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	15	19
1	15	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

675.0ms	1505×	body	1280	valid
351.0ms	1244×	body	640	valid
262.0ms	4304×	body	80	valid
125.0ms	636×	body	320	valid
45.0ms	311×	body	160	valid