Details

sample38.0ms

Algorithm

intervals

Results

8.0ms	190×	body	80	valid
4.0ms	24×	body	640	valid
3.0ms	12×	body	1280	valid
2.0ms	17×	body	320	valid
1.0ms	13×	body	160	valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5002	5

prune4.0ms

Filtered

1 candidates to 0 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: 23.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.9b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
7.5b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-exp-log` `add-cbrt-cube`
7×	`add-cube-cbrt`
5×	`pow1` `associate-l` `add-log-exp`
4×	`times-frac` `associate-l/` `associate-/r`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `associate-/l/` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `frac-2neg` `flip3-+` `diff-log` `pow-prod-down` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

9.0ms	(* (- 1.0 x) y)
10.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
12.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series32.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* (- 1.0 x) y)
16.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune190.0ms

Filtered

72 candidates to 51 candidates (29.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0.5b

Counts

73 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- 1.0 x))
0.3b	(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
2.9b	(- 1.0 (/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0)))
7.5b	(/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

68×	`cbrt-div`
37×	`*-un-lft-identity`
35×	`add-sqr-sqrt` `flip3--` `flip--`
34×	`associate-*l/`
33×	`cbrt-prod`
32×	`frac-times`
26×	`associate-/l/`
24×	`add-exp-log`
16×	`add-cbrt-cube`
15×	`add-cube-cbrt`
11×	`pow1`
10×	`associate-*r/` `swap-sqr`
9×	`prod-exp` `cbrt-unprod`
8×	`associate-r` `associate-l` `distribute-lft-out--`
7×	`pow1/3`
6×	`add-log-exp` `difference-of-squares`
5×	`cbrt-undiv` `div-exp`
4×	`times-frac` `associate-/r*` `unswap-sqr`
2×	`pow-prod-down` `associate-/r/` `pow-sqr` `pow-prod-up` `distribute-lft-out`
1×	`pow2` `sub-neg` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `clear-num` `-commutative` `flip-+` `div-inv` `associate-/l`

Counts

4 → 142

Calls

4 calls:

3.0ms	(cbrt (- 1.0 x))
13.0ms	(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
10.0ms	(- 1.0 (/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0)))
33.0ms	(/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0))

series34.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (- 1.0 x))
7.0ms	(* (cbrt (- 1.0 x)) (cbrt (- 1.0 x)))
14.0ms	(- 1.0 (/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0)))
7.0ms	(/ (* (* (cbrt (- 1.0 x)) (cbrt (- 1.0 x))) (* (cbrt (- 1.0 x)) y)) (+ y 1.0))

simplify113.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	717	1690
1	2995	1481
2	5002	1380

prune380.0ms

Filtered

154 candidates to 111 candidates (27.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	154	6	160

Merged error: 0.5b

Counts

160 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

8.2b	(cbrt (* (- 1.0 x) y))
8.2b	(cbrt (* (- 1.0 x) y))
8.2b	(cbrt (* (- 1.0 x) y))
10.5b	(- 1.0 (/ (* (* (cbrt (* (- 1.0 x) y)) (cbrt (* (- 1.0 x) y))) (cbrt (* (- 1.0 x) y))) (+ y 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `cbrt-div` `-un-lft-identity` `associate-l/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `flip3--` `add-cbrt-cube` `flip--`
3×	`cbrt-prod` `pow1/3`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 47

Calls

4 calls:

5.0ms	(cbrt (* (- 1.0 x) y))
5.0ms	(cbrt (* (- 1.0 x) y))
5.0ms	(cbrt (* (- 1.0 x) y))
7.0ms	(- 1.0 (/ (* (* (cbrt (* (- 1.0 x) y)) (cbrt (* (- 1.0 x) y))) (cbrt (* (- 1.0 x) y))) (+ y 1.0)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (* (- 1.0 x) y))
18.0ms	(cbrt (* (- 1.0 x) y))
19.0ms	(cbrt (* (- 1.0 x) y))
16.0ms	(- 1.0 (/ (* (* (cbrt (* (- 1.0 x) y)) (cbrt (* (- 1.0 x) y))) (cbrt (* (- 1.0 x) y))) (+ y 1.0)))

simplify76.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	275	816
1	750	764
2	2950	745
3	5001	745

prune187.0ms

Filtered

59 candidates to 51 candidates (13.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	59	6	65

Merged error: 0.5b

Counts

65 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
4.4b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
18.7b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
15×	`-un-lft-identity` `associate-l*`
11×	`add-cube-cbrt`
8×	`pow1` `times-frac` `associate-r`
7×	`flip3--` `flip--`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`sub-neg` `associate-*l/` `difference-of-squares`
4×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r*` `associate-/r/` `associate--r+`
2×	`frac-times` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

6.0ms	(* (- 1.0 x) y)
14.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
11.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (- 1.0 x) y)
12.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
39.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
12.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify83.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	567	1027
1	3078	900
2	5001	900

prune139.0ms

Filtered

117 candidates to 82 candidates (29.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	3	3
Picked	0	1	1
Done	1	1	2
Total	117	6	123

Merged error: 0.5b

Counts

123 → 6

regimes404.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 20.8b

bsearch29.0ms

Steps

Iters	Range		Point
5	76257442.97742975	221910749.68763962	103299873.12943959
8	-31707026623.970688	-81569296.22560106	-109848455.8215134

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	33	14

end0.0ms

sample589.0ms

Algorithm

intervals

Results

183.0ms	6112×	body	80	valid
81.0ms	701×	body	640	valid
51.0ms	366×	body	1280	valid
44.0ms	522×	body	320	valid
19.0ms	299×	body	160	valid

Details

sample38.0ms

simplify93.0ms

prune4.0ms

localize11.0ms

rewrite34.0ms

series32.0ms

simplify65.0ms

prune190.0ms

localize17.0ms

rewrite66.0ms

series34.0ms

simplify113.0ms

prune380.0ms

localize11.0ms

rewrite22.0ms

series71.0ms

simplify76.0ms

prune187.0ms

localize11.0ms

rewrite37.0ms

series70.0ms

simplify83.0ms

prune139.0ms

regimes404.0ms

bsearch29.0ms

simplify1.0ms

end0.0ms

sample589.0ms

Profiling