Details

sample504.0ms

Algorithm

intervals

Results

232.0ms	32×	body	5120	valid
100.0ms	50×	body	2560	valid
84.0ms	123×	body	1280	valid
45.0ms	88×	body	640	valid
11.0ms	36×	body	320	valid
7.0ms	62×	body	80	valid
4.0ms	18×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	44	13
1	149	13
2	869	12
3	5001	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: 37.4b

Counts

2 → 2

localize19.0ms

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)))
26.3b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite470.0ms

Algorithm

rewrite-expression-head

Rules

5057×	`add-sqr-sqrt`
2843×	`associate-l`
2812×	`unswap-sqr`
2783×	`times-frac`
2196×	`associate-r`
1235×	`unpow-prod-down`
1036×	`add-cube-cbrt` `*-un-lft-identity`
565×	`sqr-pow`
337×	`add-exp-log`
336×	`*-commutative`
328×	`swap-sqr`
220×	`prod-exp`
81×	`associate-/r*`
71×	`div-exp`
65×	`add-cbrt-cube`
51×	`pow-exp`
34×	`pow-to-exp` `cbrt-unprod`
32×	`div-inv`
28×	`associate-/l*`
12×	`pow1` `cbrt-undiv`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`tan-quot` `pow-unpow`
1×	`pow-pow` `frac-2neg` `associate-*l/` `clear-num` `associate-/r/`

Counts

4 → 2597

Calls

4 calls:

4.0ms	(pow (/ k t) 2.0)
7.0ms	(* (pow t 3.0) (tan k))
113.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
22.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series1.2s

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ k t) 2.0)
243.0ms	(* (pow t 3.0) (tan k))
378.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
463.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify555.0ms

Algorithm

egg-herbie

Counts

2609 → 2609

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5002	53914

prune7.7s

Filtered

2609 candidates to 1671 candidates (64.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	2588	21	2609
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	2590	21	2611

Merged error: 9.8b

Counts

2611 → 21

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
4.6b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
6.3b	(* (pow k 2.0) (pow t 1.0))
14.7b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite507.0ms

Algorithm

rewrite-expression-head

Rules

2158×	`add-sqr-sqrt`
1645×	`add-exp-log`
1373×	`unswap-sqr`
1368×	`times-frac`
1282×	`unpow-prod-down`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
623×	`sqr-pow`
509×	`pow-to-exp`
471×	`*-un-lft-identity`
364×	`associate-r`
285×	`unpow2`
259×	`add-cube-cbrt`
203×	`associate-l`
140×	`rec-exp` `1-exp`
45×	`associate-/l*`
44×	`associate-/r*`
31×	`associate-*r/`
27×	`*-commutative`
25×	`add-cbrt-cube`
11×	`pow1`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `un-div-inv`
2×	`pow-flip`
1×	`inv-pow`

Counts

4 → 1636

Calls

4 calls:

17.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
21.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.0ms	(* (pow k 2.0) (pow t 1.0))
262.0ms	(* (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:

338.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
91.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
341.0ms	(* (pow k 2.0) (pow t 1.0))
662.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify357.0ms

Algorithm

egg-herbie

Counts

1648 → 1648

Iterations

Useful iterations: 1 (91.0ms)

Iter	Nodes	Cost
0	4829	29271
1	5002	26595

prune3.0s

Filtered

1648 candidates to 561 candidates (34.0%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	1638	10	1648
Fresh	9	11	20
Picked	1	0	1
Done	0	0	0
Total	1648	21	1669

Merged error: 4.0b

Counts

1669 → 21

localize25.0ms

Local error

Found 4 expressions with local error:

1.4b	(/ (pow l (/ 2 2)) (pow (sin k) 2))
2.1b	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
6.3b	(* (pow k 2.0) (pow t 1.0))
7.8b	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

rewrite603.0ms

Algorithm

rewrite-expression-head

Rules

3155×	`add-sqr-sqrt`
3120×	`add-exp-log`
2362×	`prod-exp`
2251×	`unswap-sqr`
1681×	`unpow-prod-down`
1492×	`pow-exp`
1444×	`times-frac`
1052×	`div-exp`
832×	`pow-to-exp`
811×	`sqr-pow`
475×	`*-un-lft-identity`
299×	`associate-r`
234×	`associate-l`
220×	`rec-exp` `1-exp`
174×	`add-cube-cbrt`
157×	`unpow2`
34×	`add-cbrt-cube`
20×	`pow1`
18×	`associate-*r/`
16×	`associate-/r*` `cbrt-unprod`
15×	`associate-/l*`
12×	`*-commutative`
10×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num`
2×	`frac-2neg` `un-div-inv`

Counts

4 → 1902

Calls

4 calls:

10.0ms	(/ (pow l (/ 2 2)) (pow (sin k) 2))
228.0ms	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
10.0ms	(* (pow k 2.0) (pow t 1.0))
62.0ms	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (pow l (/ 2 2)) (pow (sin k) 2))
384.0ms	(* (* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0)) (/ (pow l (/ 2 2)) (pow (sin k) 2)))
326.0ms	(* (pow k 2.0) (pow t 1.0))
261.0ms	(* (* (cos k) l) (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0))

simplify391.0ms

Algorithm

egg-herbie

Counts

1914 → 1914

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5001	39155

prune3.6s

Filtered

1914 candidates to 663 candidates (34.6%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	1901	13	1914
Fresh	13	7	20
Picked	1	0	1
Done	0	0	0
Total	1915	20	1935

Merged error: 1.3b

Counts

1935 → 20

localize31.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
1.1b	(* (* (* (cos k) l) (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0)) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2))))
1.4b	(/ (pow l 1) (pow (sin k) 2))
3.9b	(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

rewrite20.6s

Algorithm

rewrite-expression-head

Rules

262474×	`add-sqr-sqrt`
204503×	`unswap-sqr`
139563×	`unpow-prod-down`
117500×	`times-frac`
67539×	`cbrt-prod`
61352×	`sqr-pow`
34113×	`*-un-lft-identity`
16036×	`add-exp-log`
11221×	`prod-exp`
9825×	`unpow2`
7800×	`swap-sqr`
7330×	`pow-exp`
5931×	`div-exp`
3758×	`pow-to-exp`
2617×	`*-commutative`
1200×	`associate-r`
887×	`associate-l`
511×	`add-cube-cbrt`
56×	`associate-*r/`
55×	`add-cbrt-cube`
52×	`associate-/r*`
29×	`associate-/l*`
28×	`cbrt-unprod`
27×	`pow1`
16×	`pow-prod-down`
9×	`cbrt-undiv`
7×	`div-inv`
6×	`clear-num`
4×	`expm1-log1p-u` `frac-2neg` `un-div-inv` `log1p-expm1-u` `add-log-exp`

Counts

4 → 46408

Calls

4 calls:

24.0ms	(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
3.9s	(* (* (* (cos k) l) (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0)) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2))))
8.0ms	(/ (pow l 1) (pow (sin k) 2))
200.0ms	(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

352.0ms	(/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0)))
403.0ms	(* (* (* (cos k) l) (pow (/ (* (cbrt 1) (cbrt 1)) (pow k (/ 2.0 2))) 1.0)) (* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2))))
72.0ms	(/ (pow l 1) (pow (sin k) 2))
457.0ms	(* (pow (/ (cbrt 1) (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0) (/ (pow l 1) (pow (sin k) 2)))

simplify24.4s

Algorithm

egg-herbie

Counts

46420 → 46420

Iterations

Useful iterations: 0 (872.0ms)

Iter	Nodes	Cost
0	34525	2596677

prune5.0m

Filtered

46420 candidates to 33822 candidates (72.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	46409	11	46420
Fresh	13	6	19
Picked	1	0	1
Done	0	0	0
Total	46423	17	46440

Merged error: 0.3b

Counts

46440 → 17

regimes482.0ms

Accuracy

12.9% (3.8b remaining)

Error of 4.0b against oracle of 0.2b and baseline of 4.6b

bsearch292.0ms

Steps

Iters	Range		Point
6	1.0418287907711792e+106	8.525507861768035e+106	2.8947889996786224e+106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	60
1	61	60
2	61	60

end0.0ms

sample13.0s

Algorithm

intervals

Results

4.1s	2158×	body	2560	valid
3.8s	898×	body	5120	valid
2.8s	4018×	body	1280	valid
1.2s	2495×	body	640	valid
338.0ms	1023×	body	320	valid
209.0ms	1985×	body	80	valid
101.0ms	431×	body	160	valid