Details

sample62.0ms

Algorithm

intervals

Results

17.0ms	276×	body	80	valid
5.0ms	109×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

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: 23.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
3.8b	(* (* x y) z)
6.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
4.0ms	(* (* x y) z)
8.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
32.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune138.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 4.9b

Counts

89 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
3.1b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 112

Calls

4 calls:

8.0ms	(/ z (sqrt (- (* z z) (* t a))))
3.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
31.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	428	1014
1	2153	912
2	5002	894

prune140.0ms

Filtered

82 candidates to 124 candidates (-51.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	123	10	133

Merged error: 4.9b

Counts

133 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.2b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.9b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
33.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	400	774
1	1768	676
2	5001	668

prune121.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	105	9	114

Merged error: 4.9b

Counts

114 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.9b	(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
5.2b	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.6b	(sqrt (- (* z z) (* t a)))
24.6b	(sqrt (- (* z z) (* t a)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
36×	`associate-l`
34×	`add-exp-log` `associate-r` `add-cbrt-cube`
16×	`unswap-sqr`
13×	`pow1` `prod-exp` `cbrt-unprod`
12×	`sqrt-div`
8×	`cbrt-undiv` `div-exp`
5×	`associate-*r/`
4×	`flip3--` `pow-prod-down` `associate-/r/` `flip--` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `div-inv`

Counts

4 → 159

Calls

4 calls:

17.0ms	(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
33.0ms	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
19.0ms	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify79.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	666	2583
1	2931	2289
2	5001	2197

prune127.0ms

Filtered

106 candidates to 171 candidates (-61.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	171	9	180

Merged error: 4.9b

Counts

180 → 9

regimes865.0ms

Accuracy

83.9% (3.2b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 22.8b

bsearch47.0ms

Steps

Iters	Range		Point
7	7.85092102435006e+87	5.871565491936595e+89	1.9550803051564794e+89
7	-1.9965387233555876e+96	-4.226289434289042e+94	-1.973163357362676e+96

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	31	10
2	31	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

458.0ms	8874×	body	80	valid
134.0ms	2870×	body	80	nan

Details

sample62.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite21.0ms

series57.0ms

simplify51.0ms

prune138.0ms

localize10.0ms

rewrite30.0ms

series61.0ms

simplify65.0ms

prune140.0ms

localize10.0ms

rewrite31.0ms

series73.0ms

simplify53.0ms

prune121.0ms

localize13.0ms

rewrite65.0ms

series78.0ms

simplify79.0ms

prune127.0ms

regimes865.0ms

bsearch47.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling