Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	243×	body	80	valid
2.0ms	17×	body	640	valid
2.0ms	16×	body	320	valid
2.0ms	9×	body	1280	valid
1.0ms	15×	body	160	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

prune4.0ms

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: 24.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
3.8b	(+ x (/ (* (- y x) (- z t)) (- a t)))
17.1b	(/ (* (- y x) (- z t)) (- a t))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

8.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
15.0ms	(/ (* (- y x) (- z t)) (- a t))

series93.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
52.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
32.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify50.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune149.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	13	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	13	91

Merged error: 6.2b

Counts

91 → 13

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.3b	(* (- y x) (/ (- z t) (- a t)))
3.8b	(+ x (* (- y x) (/ (- z t) (- a t))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

7.0ms	(/ (- z t) (- a t))
15.0ms	(* (- y x) (/ (- z t) (- a t)))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

series93.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
32.0ms	(* (- y x) (/ (- z t) (- a t)))
52.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))

simplify53.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5002	820

prune167.0ms

Filtered

82 candidates to 128 candidates (-56.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	123	18	141

Merged error: 6.1b

Counts

141 → 18

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
2.3b	(/ (- y x) (/ (- a t) (- z t)))
3.8b	(+ x (/ (- y x) (/ (- a t) (- z t))))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

10.0ms	(/ (- a t) (- z t))
14.0ms	(/ (- y x) (/ (- a t) (- z t)))
36.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

series104.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- a t) (- z t))
42.0ms	(/ (- y x) (/ (- a t) (- z t)))
53.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))

simplify101.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5001	2984

prune242.0ms

Filtered

172 candidates to 283 candidates (-64.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	10	7	17
Picked	1	0	1
Done	0	0	0
Total	286	15	301

Merged error: 5.9b

Counts

301 → 15

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a t))
0.2b	(* (- z t) (/ 1 (- a t)))
2.3b	(* (- y x) (* (- z t) (/ 1 (- a t))))
4.5b	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `un-div-inv`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 146

Calls

4 calls:

5.0ms	(/ 1 (- a t))
12.0ms	(* (- z t) (/ 1 (- a t)))
14.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
4.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

series102.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (- a t))
10.0ms	(* (- z t) (/ 1 (- a t)))
36.0ms	(* (- y x) (* (- z t) (/ 1 (- a t))))
52.0ms	(+ x (* (- y x) (* (- z t) (/ 1 (- a t)))))

simplify76.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	586	1025
1	2802	908
2	5003	863

prune128.0ms

Filtered

98 candidates to 158 candidates (-61.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	156	2	158
Fresh	3	11	14
Picked	0	1	1
Done	0	0	0
Total	159	14	173

Merged error: 5.9b

Counts

173 → 14

regimes544.0ms

Accuracy

5.8% (6.9b remaining)

Error of 10.9b against oracle of 4.0b and baseline of 11.3b

bsearch51.0ms

Steps

Iters	Range		Point
10	2.1769624338289646e-67	3.9757873648513837e-53	2.21132819556242e-67
6	-8.032711808417052e-170	-5.037938475517998e-171	-7.235102096299877e-171

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	26
1	41	26

end0.0ms

sample887.0ms

Algorithm

intervals

Results

305.0ms	7880×	body	80	valid
65.0ms	473×	body	640	valid
46.0ms	254×	body	1280	valid
46.0ms	421×	body	320	valid
19.0ms	236×	body	160	valid
4.0ms	19×	body	2560	valid

Details

sample45.0ms

simplify61.0ms

prune4.0ms

localize9.0ms

rewrite32.0ms

series93.0ms

simplify50.0ms

prune149.0ms

localize9.0ms

rewrite30.0ms

series93.0ms

simplify53.0ms

prune167.0ms

localize10.0ms

rewrite77.0ms

series104.0ms

simplify101.0ms

prune242.0ms

localize10.0ms

rewrite44.0ms

series102.0ms

simplify76.0ms

prune128.0ms

regimes544.0ms

bsearch51.0ms

simplify1.0ms

end0.0ms

sample887.0ms

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