Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	253×	body	80	valid
2.0ms	13×	body	640	valid
2.0ms	10×	body	1280	valid
1.0ms	17×	body	320	valid
0.0ms	1×	body	2560	valid
0.0ms	3×	body	160	valid

simplify54.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

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: 14.9b

Counts

2 → 2

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
2.2b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.4b	(* (- y z) (/ (- t x) (- a z)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

102×	`*-un-lft-identity`
97×	`add-sqr-sqrt`
51×	`times-frac`
34×	`add-cube-cbrt`
31×	`associate-r` `distribute-lft-out--`
30×	`frac-times`
29×	`difference-of-squares`
22×	`flip3--` `flip--` `associate-/l*`
20×	`associate-/r*`
15×	`associate-*r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l/`
7×	`associate-l`
5×	`pow1` `clear-num` `add-log-exp`
4×	`frac-2neg` `associate-/r/`
3×	`expm1-log1p-u` `fma-def` `un-div-inv` `log1p-expm1-u` `distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `flip3-+` `div-sub` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

3 → 176

Calls

3 calls:

9.0ms	(/ (- t x) (- a z))
23.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
21.0ms	(* (- y z) (/ (- t x) (- a z)))

series326.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (- t x) (- a z))
148.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
129.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify86.0ms

Algorithm

egg-herbie

Counts

185 → 185

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	655	1324
1	3300	1269
2	5001	1267

prune477.0ms

Filtered

185 candidates to 128 candidates (69.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	175	10	185
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	177	10	187

Merged error: 3.2b

Counts

187 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.0b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
8.3b	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

2246×	`cbrt-prod`
2232×	`add-sqr-sqrt`
1845×	`associate-r`
1774×	`*-un-lft-identity`
1306×	`times-frac`
796×	`swap-sqr`
693×	`add-cube-cbrt`
619×	`associate-l`
460×	`distribute-lft-out--`
458×	`unswap-sqr`
307×	`difference-of-squares`
178×	`frac-times`
108×	`flip3--` `flip--`
107×	`associate-/l*`
105×	`associate-/r*`
95×	`*-commutative`
89×	`associate-*r/`
81×	`add-cbrt-cube`
66×	`cbrt-unprod`
52×	`cbrt-div`
25×	`cbrt-undiv`
24×	`associate-/l/`
22×	`add-exp-log`
10×	`associate-*l/`
9×	`prod-exp`
8×	`associate-/r/`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `div-exp` `clear-num` `log1p-expm1-u` `distribute-lft-out`
3×	`fma-def` `frac-2neg` `un-div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `flip-+` `div-inv`

Counts

4 → 1668

Calls

4 calls:

3.0ms	(cbrt (- a z))
10.0ms	(cbrt (- a z))
323.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
1.5s	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series741.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
153.0ms	(cbrt (- a z))
278.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
157.0ms	(+ x (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify234.0ms

Algorithm

egg-herbie

Counts

1680 → 1680

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5001	24213

prune4.6s

Filtered

1680 candidates to 848 candidates (50.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	1678	2	1680
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	1679	11	1690

Merged error: 3.2b

Counts

1690 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- t x)))
0.6b	(cbrt (cbrt (- t x)))
2.7b	(* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z))))
8.3b	(+ x (* (* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite14.6s

Algorithm

rewrite-expression-head

Rules

32517×	`cbrt-prod`
31208×	`add-sqr-sqrt`
20032×	`frac-times`
14155×	`unswap-sqr`
11835×	`associate-/l*`
9402×	`associate-r`
9360×	`*-un-lft-identity`
8538×	`cbrt-div`
6148×	`flip3--` `flip--`
5809×	`associate-l`
5438×	`times-frac`
5427×	`associate-/r*`
4724×	`associate-*r/`
4714×	`add-cube-cbrt`
2838×	`associate-/l/`
2236×	`swap-sqr`
1778×	`distribute-lft-out--`
1577×	`difference-of-squares`
1254×	`add-cbrt-cube`
1235×	`cbrt-unprod`
1095×	`associate-*l/`
681×	`*-commutative`
545×	`clear-num`
519×	`frac-2neg`
503×	`cbrt-undiv`
88×	`add-exp-log`
77×	`un-div-inv`
48×	`prod-exp`
20×	`div-exp`
9×	`pow1`
6×	`add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 15636

Calls

4 calls:

4.0ms	(cbrt (cbrt (- t x)))
4.0ms	(cbrt (cbrt (- t x)))
3.2s	(* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z))))
8.1s	(+ x (* (* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (cbrt (- t x)))
142.0ms	(cbrt (cbrt (- t x)))
274.0ms	(* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z))))
531.0ms	(+ x (* (* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify5.1s

Algorithm

egg-herbie

Counts

15648 → 15648

Iterations

Useful iterations: 0 (204.0ms)

Iter	Nodes	Cost
0	16724	627631

prune1.6m

Filtered

15648 candidates to 11630 candidates (74.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	15647	1	15648
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	15648	11	15659

Merged error: 3.2b

Counts

15659 → 11

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- t x)))
0.6b	(cbrt (cbrt (- t x)))
2.7b	(* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z))))
10.3b	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite6.3s

Algorithm

rewrite-expression-head

Rules

32517×	`cbrt-prod`
31207×	`add-sqr-sqrt`
20032×	`frac-times`
14155×	`unswap-sqr`
11835×	`associate-/l*`
9402×	`associate-r`
9348×	`*-un-lft-identity`
8538×	`cbrt-div`
6148×	`flip3--` `flip--`
5800×	`associate-l`
5438×	`times-frac`
5427×	`associate-/r*`
4724×	`associate-*r/`
4713×	`add-cube-cbrt`
2838×	`associate-/l/`
2236×	`swap-sqr`
1777×	`distribute-lft-out--`
1577×	`difference-of-squares`
1254×	`add-cbrt-cube`
1235×	`cbrt-unprod`
1095×	`associate-*l/`
681×	`*-commutative`
545×	`clear-num`
519×	`frac-2neg`
503×	`cbrt-undiv`
88×	`add-exp-log`
77×	`un-div-inv`
48×	`prod-exp`
20×	`div-exp`
9×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`pow1/3` `div-inv`
1×	`fma-udef`

Counts

4 → 15625

Calls

4 calls:

4.0ms	(cbrt (cbrt (- t x)))
4.0ms	(cbrt (cbrt (- t x)))
3.2s	(* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z))))
1.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (cbrt (- t x)))
146.0ms	(cbrt (cbrt (- t x)))
268.0ms	(* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z))))
153.0ms	(fma (* (cbrt x) (cbrt x)) (cbrt x) (* (* (* (- y z) (/ (* (cbrt (- t x)) (* (cbrt (cbrt (- t x))) (cbrt (cbrt (- t x))))) (* (cbrt (- a z)) (cbrt 1)))) (/ (cbrt (cbrt (- t x))) (cbrt (- a z)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

simplify5.4s

Algorithm

egg-herbie

Counts

15637 → 15637

Iterations

Useful iterations: 0 (183.0ms)

Iter	Nodes	Cost
0	16714	627270

prune1.7m

Filtered

15637 candidates to 11624 candidates (74.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	15635	2	15637
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	15636	12	15648

Merged error: 3.2b

Counts

15648 → 12

regimes351.0ms

Accuracy

16% (8.6b remaining)

Error of 12.3b against oracle of 3.7b and baseline of 13.9b

bsearch182.0ms

Steps

Iters	Range	Point
9	7.0067478635952275e+121	1.0573135039252488e+128	9.704798279387757e+127
10	-2.702832232841147e-161	-3.8275097991180148e-171	-1.061022533733094e-165
9	-2.9973561627917858e+172	-7.373635255817937e+164	-2.610591643114714e+171

Iters

Range

Point

7.0067478635952275e+121

1.0573135039252488e+128

9.704798279387757e+127

-2.702832232841147e-161

-3.8275097991180148e-171

-1.061022533733094e-165

-2.9973561627917858e+172

-7.373635255817937e+164

-2.610591643114714e+171

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	51
1	51	51

end0.0ms

sample725.0ms

Algorithm

intervals

Results

265.0ms	7786×	body	80	valid
60.0ms	512×	body	640	valid
41.0ms	263×	body	1280	valid
39.0ms	411×	body	320	valid
14.0ms	223×	body	160	valid
4.0ms	21×	body	2560	valid