Details

sample61.0ms

Algorithm

intervals

Results

12.0ms	44×	body	2560	valid
9.0ms	188×	body	80	valid
7.0ms	33×	body	1280	valid
5.0ms	105×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune5.0ms

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: 36.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(- (* b b) (* (* 3.0 a) c))
1.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
27.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
9.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune407.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 5.9b

Counts

83 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
11.3b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
27.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

10.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series136.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
60.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	644	2693
1	3143	2447
2	5001	2434

prune992.0ms

Filtered

166 candidates to 111 candidates (33.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	166	11	177

Merged error: 5.8b

Counts

177 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

8.9b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
10.7b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
27.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
27.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `sqrt-prod` `add-cbrt-cube`
5×	`difference-of-squares`
4×	`flip3--` `sqrt-div` `associate-/r*` `flip--`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv`

Counts

4 → 80

Calls

4 calls:

4.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
7.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
56.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	404	1607
1	1915	1363
2	5001	1321

prune766.0ms

Filtered

92 candidates to 79 candidates (14.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	92	11	103

Merged error: 5.8b

Counts

103 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

5.5b	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.8b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))))
16.5b	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
27.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-cube-cbrt`
16×	`log-prod` `exp-sum`
15×	`difference-of-squares`
11×	`sqrt-prod`
10×	`distribute-lft-out--`
8×	`associate-/r*` `add-log-exp`
7×	`pow1`
6×	`add-exp-log` `exp-prod` `add-cbrt-cube`
5×	`distribute-rgt-neg-in`
4×	`flip3--` `sqrt-div` `flip--`
3×	`log-pow` `associate-/l*`
2×	`log-div` `sqrt-pow1` `pow1/2` `exp-diff` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `frac-2neg` `flip3-+` `div-exp` `neg-log` `clear-num` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 107

Calls

4 calls:

6.0ms	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))))
10.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))
60.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c)))))))
15.0ms	(- (neg b) (exp (log (sqrt (- (* b b) (* (* 3.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify84.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	447	1710
1	1931	1548
2	5001	1516

prune779.0ms

Filtered

119 candidates to 83 candidates (30.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	119	11	130

Merged error: 5.8b

Counts

130 → 11

regimes844.0ms

Accuracy

82.8% (4.7b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 32.8b

bsearch164.0ms

Steps

Iters	Range		Point
9	1.4958858181332487e-84	1.457638978688563e-75	4.353250150025503e-84
10	-8.56091843340189e+161	-1.1976703346365243e+147	-9.079265283465152e+151

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	17
1	37	17

end0.0ms

sample1.6s

Algorithm

intervals

Results

302.0ms	1091×	body	2560	valid
280.0ms	5797×	body	80	valid
204.0ms	909×	body	1280	valid
131.0ms	2913×	body	80	nan
90.0ms	497×	body	640	valid
41.0ms	114×	body	5120	valid
30.0ms	231×	body	320	valid
8.0ms	91×	body	160	valid

Details

sample61.0ms

simplify11.0ms

prune5.0ms

localize11.0ms

rewrite32.0ms

series65.0ms

simplify52.0ms

prune407.0ms

localize15.0ms

rewrite50.0ms

series136.0ms

simplify125.0ms

prune992.0ms

localize18.0ms

rewrite21.0ms

series106.0ms

simplify81.0ms

prune766.0ms

localize20.0ms

rewrite42.0ms

series105.0ms

simplify84.0ms

prune779.0ms

regimes844.0ms

bsearch164.0ms

simplify1.0ms

end0.0ms

sample1.6s

Profiling