Details

analyze581.0ms

Algorithm

sampling

Space saved by range analysis: 99.998267%

Space saved by search: 99.999093%

Guaranteed chance to sample good point: 88.065532%

sample44.0ms

Algorithm

intervals

Results

15.0ms	160×	body	160	valid
8.0ms	38×	body	320	valid
7.0ms	267×	pre	80	true
3.0ms	58×	body	80	valid
1.0ms	11×	body	80	nan

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

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: 43.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
37.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite30.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune130.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.2b

Counts

83 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 151

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
63.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	643	2666
1	3210	2408
2	5001	2396

prune312.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	158	10	168

Merged error: 0.0b

Counts

168 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
0.3b	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
0.5b	(* (* b b) (* b b))
0.7b	(pow (* (* 4.0 a) c) 3)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

121×	`pow1`
89×	`add-sqr-sqrt`
58×	`times-frac`
57×	`*-un-lft-identity`
36×	`pow-prod-up` `difference-of-squares`
33×	`add-cube-cbrt`
26×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
22×	`pow-sqr`
21×	`sqr-pow`
18×	`pow-plus`
13×	`pow2` `associate-/l*`
12×	`distribute-lft-out--`
11×	`prod-exp` `associate-/r*` `cbrt-unprod`
9×	`unpow-prod-down`
8×	`sqrt-prod`
4×	`distribute-rgt-neg-in` `associate-/r/` `associate-/l/` `add-log-exp`
3×	`pow-unpow` `pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`
1×	`cube-mult` `pow-to-exp` `unpow3` `div-sub` `cube-prod` `swap-sqr` `associate-r` `associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 199

Calls

4 calls:

46.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
24.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
9.0ms	(* (* b b) (* b b))
8.0ms	(pow (* (* 4.0 a) c) 3)

series147.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
34.0ms	(/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
3.0ms	(* (* b b) (* b b))
9.0ms	(pow (* (* 4.0 a) c) 3)

simplify167.0ms

Algorithm

egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	785	3873
1	3938	3628
2	5001	3623

prune610.0ms

Filtered

118 candidates to 211 candidates (-78.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	209	2	211
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	211	10	221

Merged error: 0.0b

Counts

221 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 6) (* (pow (* 4.0 a) 3) (pow c 3))) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
0.3b	(* (pow (* 4.0 a) 3) (pow c 3))
0.3b	(/ (- (pow b 6) (* (pow (* 4.0 a) 3) (pow c 3))) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
0.5b	(* (* b b) (* b b))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

115×	`pow1`
67×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
40×	`add-exp-log`
37×	`times-frac`
36×	`pow-prod-up`
29×	`add-cube-cbrt`
24×	`pow-prod-down`
23×	`prod-exp`
22×	`pow-sqr` `add-cbrt-cube`
18×	`pow-plus`
13×	`pow2` `associate-r`
12×	`difference-of-squares`
11×	`associate-/r*`
10×	`pow-exp`
9×	`associate-l` `cbrt-unprod` `unswap-sqr`
8×	`sqrt-prod` `distribute-lft-out--` `sqr-pow`
7×	`pow-to-exp`
6×	`unpow-prod-down` `cube-prod` `associate-/l*`
4×	`distribute-rgt-neg-in` `associate-/r/` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `cube-mult` `flip3--` `frac-2neg` `flip3-+` `unpow3` `div-exp` `clear-num` `*-commutative` `flip--` `flip-+` `div-inv`
1×	`div-sub` `swap-sqr`

Counts

4 → 196

Calls

4 calls:

32.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 6) (* (pow (* 4.0 a) 3) (pow c 3))) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
9.0ms	(* (pow (* 4.0 a) 3) (pow c 3))
20.0ms	(/ (- (pow b 6) (* (pow (* 4.0 a) 3) (pow c 3))) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
9.0ms	(* (* b b) (* b b))

series153.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 6) (* (pow (* 4.0 a) 3) (pow c 3))) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))
13.0ms	(* (pow (* 4.0 a) 3) (pow c 3))
37.0ms	(/ (- (pow b 6) (* (pow (* 4.0 a) 3) (pow c 3))) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b))))
3.0ms	(* (* b b) (* b b))

simplify160.0ms

Algorithm

egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	757	3274
1	4130	3017
2	5001	2989

prune669.0ms

Filtered

115 candidates to 208 candidates (-80.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	206	2	208
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Merged error: 0b

Counts

218 → 9

regimes249.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	37
1	45	37
2	45	37

end0.0ms

analyze575.0ms

Algorithm

sampling

Space saved by range analysis: 99.998267%

Space saved by search: 99.999093%

Guaranteed chance to sample good point: 88.065532%

sample1.2s

Algorithm

intervals

Results

473.0ms	4832×	body	160	valid
250.0ms	8535×	pre	80	true
197.0ms	1354×	body	320	valid
90.0ms	1814×	body	80	valid
26.0ms	535×	body	80	nan

Details

analyze581.0ms

sample44.0ms

simplify10.0ms

prune4.0ms

localize12.0ms

rewrite30.0ms

series68.0ms

simplify44.0ms

prune130.0ms

localize15.0ms

rewrite49.0ms

series135.0ms

simplify112.0ms

prune312.0ms

localize27.0ms

rewrite98.0ms

series147.0ms

simplify167.0ms

prune610.0ms

localize31.0ms

rewrite78.0ms

series153.0ms

simplify160.0ms

prune669.0ms

regimes249.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze575.0ms

sample1.2s

Profiling