Details

sample424.0ms

Algorithm

intervals

Results

124.0ms	73×	body	2560	valid
115.0ms	146×	body	1280	valid
103.0ms	26×	body	5120	valid
37.0ms	75×	body	640	valid
11.0ms	32×	body	320	valid
8.0ms	70×	body	80	valid
4.0ms	18×	body	160	valid

simplify27.0ms

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

prune11.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 37.0b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ k t) 2.0)
0.8b	(* (pow t 3.0) (tan k))
18.2b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
28.7b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

337×	`add-exp-log`
220×	`prod-exp`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
24×	`associate-l`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
12×	`cbrt-undiv`
5×	`pow1` `associate-*r/`
4×	`associate-r` `add-log-exp` `sqr-pow`
3×	`tan-quot` `pow-unpow` `div-inv` `unswap-sqr`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
5.0ms	(* (pow t 3.0) (tan k))
17.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series906.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(pow (/ k t) 2.0)
233.0ms	(* (pow t 3.0) (tan k))
364.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
245.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify138.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	974	1954
1	4995	1620
2	5001	1620

prune418.0ms

Filtered

191 candidates to 88 candidates (46.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	9	193

Merged error: 20.1b

Counts

193 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
5.5b	(* (pow k 2.0) (pow t 1.0))
14.2b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite106.0ms

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:

10.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.0ms	(* (pow k 2.0) (pow t 1.0))
21.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
327.0ms	(* (pow k 2.0) (pow t 1.0))
647.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify164.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1316	7192
1	4162	7023
2	5002	7016

prune579.0ms

Filtered

612 candidates to 99 candidates (16.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	599	13	612
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	606	15	621

Merged error: 15.9b

Counts

621 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.7b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
14.2b	(* (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)))

rewrite261.0ms

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:

2.0ms	(pow (sin k) 2)
12.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
42.0ms	(* (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:

18.0ms	(pow (sin k) 2)
343.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
88.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
654.0ms	(* (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)))

simplify310.0ms

Algorithm

egg-herbie

Counts

1472 → 1472

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1742	23541
1	4574	19109
2	5002	17856

prune509.0ms

Filtered

1472 candidates to 84 candidates (5.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	1465	7	1472
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	1473	14	1487

Merged error: 11.5b

Counts

1487 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
2.2b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
11.2b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

25023×	`add-exp-log`
19197×	`prod-exp`
16899×	`pow-exp`
11140×	`div-exp`
7959×	`pow-to-exp`
2990×	`rec-exp` `1-exp`
51×	`unpow-prod-down`
43×	`times-frac`
40×	`associate-l`
37×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cbrt-unprod`
13×	`associate-r`
9×	`associate-/r*` `sqr-pow`
8×	`cbrt-undiv`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`associate-*r/` `unpow2` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 5762

Calls

4 calls:

7.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
96.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
8.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
26.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

335.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
645.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2))))
85.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
637.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.1s

Algorithm

egg-herbie

Counts

5774 → 5774

Iterations

Useful iterations: 1 (68.0ms)

Iter	Nodes	Cost
0	4423	106455
1	5002	106273

prune724.0ms

Filtered

5774 candidates to 118 candidates (2.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	5770	4	5774
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	5773	15	5788

Merged error: 11.4b

Counts

5788 → 15

regimes373.0ms

Accuracy

40.4% (2.7b remaining)

Error of 15.9b against oracle of 13.2b and baseline of 17.7b

bsearch476.0ms

Steps

Iters	Range		Point
9	5.3304778821599005e-36	1.7151173105153584e-26	1.913294715595122e-35
6	-3.644302906869421e-88	-3.979740892597312e-89	-9.020397901722467e-89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	56
1	61	56

end0.0ms

sample13.9s

Algorithm

intervals

Results

4.4s	2268×	body	2560	valid
3.7s	944×	body	5120	valid
3.1s	4016×	body	1280	valid
1.5s	2512×	body	640	valid
380.0ms	1049×	body	320	valid
252.0ms	2053×	body	80	valid
107.0ms	441×	body	160	valid

Details

sample424.0ms

simplify27.0ms

prune11.0ms

localize24.0ms

rewrite49.0ms

series906.0ms

simplify138.0ms

prune418.0ms

localize23.0ms

rewrite106.0ms

series1.4s

simplify164.0ms

prune579.0ms

localize25.0ms

rewrite261.0ms

series1.1s

simplify310.0ms

prune509.0ms

localize28.0ms

rewrite1.3s

series1.7s

simplify1.1s

prune724.0ms

regimes373.0ms

bsearch476.0ms

simplify2.0ms

end0.0ms

sample13.9s

Profiling