Details

sample318.0ms

Algorithm

intervals

Results

20.0ms	42×	body	1280	valid
13.0ms	146×	body	80	valid
12.0ms	38×	body	640	valid
8.0ms	22×	body	320	valid
1.0ms	8×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))) (+ 1.0 (* (tan x) (tan x))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite27.0ms

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:

8.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
2.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
8.0ms	(* (tan x) (tan x))

series216.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
38.0ms	(- 1.0 (* (tan x) (tan x)))
31.0ms	(* (tan x) (tan x))
55.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	338	1007
1	1243	918
2	5001	882

prune292.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
8×	`tan-quot` `add-exp-log` `add-cbrt-cube`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u`
3×	`fma-neg` `prod-diff`
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×	`sub-neg` `log1p-udef` `flip3--` `diff-log` `log1p-expm1` `flip--` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

2.0ms	(- 1.0 (* (tan x) (tan x)))
0.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
5.0ms	(* (tan x) (tan x))
5.0ms	(* (tan x) (tan x))

series316.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- 1.0 (* (tan x) (tan x)))
219.0ms	(log1p (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
32.0ms	(* (tan x) (tan x))
32.0ms	(* (tan x) (tan x))

simplify135.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (128.0ms)

Iter	Nodes	Cost
0	246	612
1	827	546
2	3958	530
3	5002	525

prune256.0ms

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	(pow (cos x) 2)
0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
2.0ms	(pow (sin x) 2)

series74.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (cos x) 2)
20.0ms	(pow (cos x) 2)
19.0ms	(pow (sin x) 2)
19.0ms	(pow (sin x) 2)

simplify61.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	146	308
1	487	260
2	1671	260
3	5001	256

prune248.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)
2.9b	(log (exp (pow (sin x) 2)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`pow-unpow` `log-pow`
8×	`pow1` `exp-prod`
7×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `unpow2` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `log-prod` `pow-pow` `pow-exp`
1×	`rem-log-exp`

Counts

4 → 82

Calls

4 calls:

1.0ms	(pow (cos x) 2)
1.0ms	(pow (sin x) 2)
1.0ms	(pow (sin x) 2)
7.0ms	(log (exp (pow (sin x) 2)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(pow (cos x) 2)
18.0ms	(pow (sin x) 2)
18.0ms	(pow (sin x) 2)
19.0ms	(log (exp (pow (sin x) 2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	184	327
1	552	275
2	1829	275
3	5001	271

prune273.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes196.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	17
1	17	17

end0.0ms

sample1.9s

Algorithm

intervals

Results

754.0ms	1496×	body	1280	valid
400.0ms	4356×	body	80	valid
390.0ms	1218×	body	640	valid
143.0ms	619×	body	320	valid
50.0ms	311×	body	160	valid