Details

sample538.0ms

Algorithm

intervals

Results

125.0ms	52×	body	2560	valid
53.0ms	85×	body	1280	valid
44.0ms	63×	body	640	valid
6.0ms	25×	body	320	valid
4.0ms	17×	body	160	valid
1.0ms	14×	body	80	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.7b	(- x (tan x))
1.7b	(- x (sin x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
15×	`add-cube-cbrt`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 80

Calls

3 calls:

23.0ms	(/ (- x (sin x)) (- x (tan x)))
5.0ms	(- x (tan x))
9.0ms	(- x (sin x))

series164.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(/ (- x (sin x)) (- x (tan x)))
55.0ms	(- x (tan x))
39.0ms	(- x (sin x))

simplify151.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	363	718
1	1148	685
2	4795	685
3	5001	685

prune198.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 27/2800 (pow x 4))
0.2b	(* 9/40 (pow x 2))
16.3b	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`associate-r`
13×	`add-exp-log`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-log-exp`
7×	`add-cbrt-cube` `unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`sqr-pow`
3×	`pow1`
2×	`pow-to-exp` `diff-log` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 66

Calls

3 calls:

11.0ms	(* 27/2800 (pow x 4))
12.0ms	(* 9/40 (pow x 2))
21.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

series100.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(* 27/2800 (pow x 4))
23.0ms	(* 9/40 (pow x 2))
44.0ms	(- (* 9/40 (pow x 2)) (+ (* 27/2800 (pow x 4)) 1/2))

simplify42.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	273	349
1	1123	318
2	5001	315

prune139.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin x) (sin x))
1.7b	(- x (tan x))
1.7b	(- (* x x) (* (sin x) (sin x)))
15.8b	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

12.0ms	(* (sin x) (sin x))
5.0ms	(- x (tan x))
10.0ms	(- (* x x) (* (sin x) (sin x)))
31.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sin x) (sin x))
49.0ms	(- x (tan x))
56.0ms	(- (* x x) (* (sin x) (sin x)))
138.0ms	(/ (- (* x x) (* (sin x) (sin x))) (* (- x (tan x)) (+ x (sin x))))

simplify73.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	565	877
1	2896	760
2	5001	756

prune243.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (* x x) (* (sin x) (sin x)))
15.2b	(sqrt (- (* x x) (* (sin x) (sin x))))
15.2b	(sqrt (- (* x x) (* (sin x) (sin x))))
15.8b	(/ (* (sqrt (- (* x x) (* (sin x) (sin x)))) (sqrt (- (* x x) (* (sin x) (sin x))))) (* (- x (tan x)) (+ x (sin x))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
12×	`flip3--` `flip--`
8×	`add-sqr-sqrt` `frac-times` `sqrt-prod` `associate-/r/` `associate-/l/`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`cbrt-undiv` `associate-r/` `div-exp` `associate-l/` `prod-exp` `cbrt-unprod`
3×	`flip3-+` `flip-+` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `sqr-sin` `div-inv` `associate-/l` `associate--r-`

Counts

4 → 83

Calls

4 calls:

10.0ms	(- (* x x) (* (sin x) (sin x)))
9.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
9.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
47.0ms	(/ (* (sqrt (- (* x x) (* (sin x) (sin x)))) (sqrt (- (* x x) (* (sin x) (sin x))))) (* (- x (tan x)) (+ x (sin x))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* x x) (* (sin x) (sin x)))
75.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
74.0ms	(sqrt (- (* x x) (* (sin x) (sin x))))
137.0ms	(/ (* (sqrt (- (* x x) (* (sin x) (sin x)))) (sqrt (- (* x x) (* (sin x) (sin x))))) (* (- x (tan x)) (+ x (sin x))))

simplify67.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	566	1348
1	2785	1113
2	5001	1100

prune309.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes54.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 30.7b

bsearch75.0ms

Steps

Iters	Range		Point
8	0.00015704816827310668	9.114942375872904	0.01861232521167047
9	-0.2945747773639613	-3.489101517161873e-08	-0.024389077621678308

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	11
1	29	11

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.5s	1584×	body	2560	valid
1.9s	2847×	body	1280	valid
631.0ms	1840×	body	640	valid
216.0ms	907×	body	320	valid
69.0ms	445×	body	160	valid
35.0ms	377×	body	80	valid