Details

sample615.0ms

Algorithm

intervals

Results

234.0ms	75×	body	640	valid
118.0ms	67×	body	2560	valid
112.0ms	125×	body	1280	valid
104.0ms	27×	body	5120	valid
15.0ms	40×	body	320	valid
7.0ms	57×	body	80	valid
3.0ms	12×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
0.6b	(* (pow t 3.0) (tan k))
19.1b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
31.0b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-exp-log`
265×	`prod-exp`
74×	`div-exp` `add-cbrt-cube`
61×	`pow-exp`
41×	`pow-to-exp`
40×	`cbrt-unprod`
25×	`associate-l`
21×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv`
10×	`times-frac`
7×	`associate-r/` `associate-r*`
6×	`pow1`
4×	`tan-quot` `add-log-exp`
3×	`*-commutative` `unswap-sqr` `sqr-pow`
2×	`associate-*l/` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 185

Calls

4 calls:

83.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
16.0ms	(* (pow t 3.0) (tan k))
90.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
44.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.1s

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
231.0ms	(* (pow t 3.0) (tan k))
345.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
233.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify123.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	908	2174
1	4774	1790
2	5002	1790

prune630.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 21.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.4b	(* (pow k 2.0) (pow t 1.0))
14.4b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

18.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.0ms	(* (pow k 2.0) (pow t 1.0))
71.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

314.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
81.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
320.0ms	(* (pow k 2.0) (pow t 1.0))
597.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify153.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1316	7194
1	4162	7025
2	5002	7018

prune886.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
4.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.4b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

4.0ms	(pow (sin k) 2)
45.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
135.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

17.0ms	(pow (sin k) 2)
330.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
84.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
618.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify280.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	1742	23543
1	4574	19111
2	5002	17858

prune844.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (sin k))
0.8b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
1.5b	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
14.4b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

3841×	`add-exp-log`
2622×	`prod-exp`
1370×	`div-exp`
1330×	`pow-exp`
679×	`pow-to-exp`
248×	`rec-exp` `1-exp`
99×	`times-frac`
80×	`add-sqr-sqrt`
65×	`add-cbrt-cube`
59×	`add-cube-cbrt` `*-un-lft-identity`
45×	`associate-r`
24×	`associate-l`
22×	`cbrt-undiv` `cbrt-unprod`
8×	`div-inv`
7×	`pow1` `unpow-prod-down`
6×	`associate-/l*` `unswap-sqr`
5×	`associate-*r/`
4×	`associate-/r*` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `associate-/r/` `inv-pow` `sqr-pow`

Counts

4 → 931

Calls

4 calls:

9.0ms	(/ (cos k) (sin k))
45.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
42.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
144.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

series1.0s

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (cos k) (sin k))
329.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
83.0ms	(* (/ (cos k) (sin k)) (/ l (/ (sin k) l)))
618.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ l (/ (sin k) l))))

simplify159.0ms

Algorithm

egg-herbie

Counts

943 → 943

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	2147	15097
1	5002	12259

prune1.3s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.4b

regimes506.0ms

Accuracy

44.8% (3.9b remaining)

Error of 12.7b against oracle of 8.8b and baseline of 15.8b

bsearch1.0s

Steps

Iters	Range		Point
2	2.7899072198473897e+125	3.056818534164292e+125	3.023454619874679e+125
7	1.9440892221314225e-121	4.330596498551672e-119	1.1036760816000066e-119
7	-4.225921979679511e-60	-1.8106102694970993e-62	-1.8403716351265589e-62
8	-6.979187882260693e+171	-3.258889053871137e+168	-3.2997205204058684e+168

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	89
1	85	89

end0.0ms

sample14.3s

Algorithm

intervals

Results

4.2s	2221×	body	2560	valid
4.0s	952×	body	5120	valid
3.5s	4045×	body	1280	valid
1.4s	2540×	body	640	valid
382.0ms	995×	body	320	valid
251.0ms	1958×	body	80	valid
112.0ms	443×	body	160	valid