Details

sample24.0ms

Algorithm

intervals

Results

7.0ms	233×	body	80	valid
2.0ms	12×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	6×	body	160	valid

simplify122.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.9b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.5b	(- (+ x y) (/ (* (- z t) y) (- a t)))
11.2b	(/ (* (- z t) y) (- a t))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
9.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.0ms	(/ (* (- z t) y) (- a t))

series238.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (- z t) y)
147.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
64.0ms	(/ (* (- z t) y) (- a t))

simplify47.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune180.0ms

Filtered

79 candidates to 56 candidates (70.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 4.5b

Counts

80 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.5b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
7.1b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `frac-times` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 127

Calls

4 calls:

6.0ms	(cbrt (- a t))
5.0ms	(cbrt (- a t))
39.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- a t))
138.0ms	(cbrt (- a t))
92.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
113.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	785	1736
1	3321	1577
2	5002	1498

prune405.0ms

Filtered

139 candidates to 105 candidates (75.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	135	4	139
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	137	12	149

Merged error: 4.5b

Counts

149 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
5.2b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
5.2b	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
7.8b	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

297×	`cbrt-div`
261×	`frac-times`
153×	`associate-*l/`
129×	`associate-*r/`
126×	`frac-sub`
63×	`flip3-+` `flip-+`
9×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `pow1/3`
2×	`diff-log`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

4 → 176

Calls

4 calls:

18.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
18.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
21.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
23.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

series974.0ms

Counts

4 → 12

Calls

4 calls:

275.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
270.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
272.0ms	(cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))
156.0ms	(- (+ x y) (* (* (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))) (cbrt (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))))

simplify159.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1756	9997
1	4189	9460
2	5001	9279

prune530.0ms

Filtered

188 candidates to 95 candidates (50.5%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	186	14	200

Merged error: 4.5b

Counts

200 → 14

localize9.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (+ x y) (* (- z t) (/ y (- a t))))
9.7b	(* (- z t) (/ y (- a t)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 70

Calls

2 calls:

7.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
13.0ms	(* (- z t) (/ y (- a t)))

series167.0ms

Counts

2 → 6

Calls

2 calls:

105.0ms	(- (+ x y) (* (- z t) (/ y (- a t))))
62.0ms	(* (- z t) (/ y (- a t)))

simplify63.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	531	657
1	2489	625
2	5001	625

prune159.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	3	8	11
Picked	0	1	1
Done	0	2	2
Total	77	13	90

Merged error: 4.5b

Counts

90 → 13

regimes329.0ms

Accuracy

25.3% (5.6b remaining)

Error of 10.0b against oracle of 4.4b and baseline of 11.9b

bsearch81.0ms

Steps

Iters	Range		Point
7	1.1800431243690469e-223	4.9448764730671337e-222	4.8862788163009955e-222
9	-7.926945014889025e-163	-1.3673509297947507e-168	-5.953855711490656e-163

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	22
1	30	22

end0.0ms

sample664.0ms

Algorithm

intervals

Results

249.0ms	7322×	body	80	valid
54.0ms	467×	body	640	valid
42.0ms	270×	body	1280	valid
36.0ms	404×	body	320	valid
15.0ms	253×	body	160	valid
3.0ms	14×	body	2560	valid