Details

sample193.0ms

Algorithm

intervals

Results

118.0ms	92×	body	2560	valid
42.0ms	80×	body	1280	valid
13.0ms	53×	body	640	valid
3.0ms	256×	pre	80	true
3.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	3×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 59.9b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
3.1b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`times-frac`
12×	`add-cube-cbrt`
5×	`distribute-lft-out--`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
3×	`associate-/r` `div-inv` `associate-/l`
2×	`pow1`
1×	`tan-quot` `cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `associate-/r/` `frac-sub` `flip--`

Counts

2 → 50

Calls

2 calls:

7.0ms	(/ 1.0 (tan x))
36.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series147.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(/ 1.0 (tan x))
109.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	232	342
1	610	327
2	1894	327
3	5001	326

prune130.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.0b	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.0021164021164021165 (pow x 5))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`associate-r`
14×	`add-exp-log`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp`
4×	`pow1` `cube-prod` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`cube-mult` `associate-+r+` `unpow3`

Counts

4 → 80

Calls

4 calls:

11.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
21.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
12.0ms	(* 0.022222222222222223 (pow x 3))
12.0ms	(* 0.0021164021164021165 (pow x 5))

series307.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
62.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
44.0ms	(* 0.022222222222222223 (pow x 3))
53.0ms	(* 0.0021164021164021165 (pow x 5))

simplify51.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	355	465
1	1532	436
2	5001	436

prune210.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.0021164021164021165 (pow x 5))
1.2b	(log (exp (* 0.022222222222222223 (pow x 3))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`associate-r`
16×	`*-un-lft-identity`
14×	`add-exp-log`
13×	`add-cube-cbrt`
8×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`cube-prod` `log-pow` `sqr-pow`
3×	`associate-+l+` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `cube-mult` `associate-+r+` `exp-prod` `exp-to-pow` `flip3-+` `unpow3` `rem-log-exp` `flip-+`

Counts

4 → 88

Calls

4 calls:

26.0ms	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
13.0ms	(* 0.022222222222222223 (pow x 3))
11.0ms	(* 0.0021164021164021165 (pow x 5))
3.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

series205.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (log (exp (* 0.022222222222222223 (pow x 3)))) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
39.0ms	(* 0.022222222222222223 (pow x 3))
56.0ms	(* 0.0021164021164021165 (pow x 5))
40.0ms	(log (exp (* 0.022222222222222223 (pow x 3))))

simplify45.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	329	521
1	1345	468
2	5001	462

prune255.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
0.6b	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

133.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
18.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
16.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

series1.2s

Counts

4 → 12

Calls

4 calls:

323.0ms	(* (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))) (cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))))
283.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
283.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
282.0ms	(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))

simplify65.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	496	2207
1	1932	2080
2	5001	1862

prune356.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

regimes85.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	18	7

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.4s	3267×	body	2560	valid
1.4s	2535×	body	1280	valid
325.0ms	1265×	body	640	valid
105.0ms	8000×	pre	80	true
96.0ms	584×	body	320	valid
43.0ms	302×	body	160	valid
3.0ms	47×	body	80	valid