Details

sample47.0ms

Algorithm

intervals

Results

11.0ms	45×	body	2560	valid
11.0ms	196×	body	80	valid
5.0ms	23×	body	1280	valid
4.0ms	96×	body	80	nan
2.0ms	10×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	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	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 35.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series212.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 3.0 a) c)
42.0ms	(- (* b b) (* (* 3.0 a) c))
77.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune220.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 14.0b

Counts

93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))
10.4b	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

72×	`sqrt-prod`
53×	`add-sqr-sqrt`
34×	`sqrt-pow1`
29×	`pow1`
28×	`sqrt-div`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1/2`
15×	`swap-sqr`
10×	`fma-def`
9×	`associate-r` `associate-l` `pow-prod-up` `unswap-sqr`
8×	`flip3--` `flip--` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
2×	`rem-sqrt-square` `associate-r/` `associate-l/` `sum-log`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `pow-plus` `sqrt-unprod` `neg-log` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 144

Calls

4 calls:

15.0ms	(* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms	(+ (- 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)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))))
78.0ms	(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	356	1458
1	1500	1280
2	5001	1245

prune306.0ms

Filtered

156 candidates to 92 candidates (59.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	154	8	162

Merged error: 13.9b

Counts

162 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
5.1b	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
8.9b	(/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
114×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
74×	`add-cube-cbrt`
45×	`associate-/l*`
40×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
20×	`distribute-lft-out`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
10×	`neg-mul-1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `distribute-neg-frac` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv`
3×	`sqrt-prod` `associate-/l/`
2×	`flip3--` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `flip--` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 208

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
11.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* b b) (* (* 3.0 a) c))
143.0ms	(/ (/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))))) (* 3.0 a))
173.0ms	(/ (+ 0 (* (* 3.0 a) c)) (- (+ b (sqrt (- (* b b) (* (* 3.0 a) c))))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 2 (104.0ms)

Iter	Nodes	Cost
0	821	3561
1	4047	3312
2	5001	3306

prune542.0ms

Filtered

220 candidates to 167 candidates (75.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	210	10	220
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	213	15	228

Merged error: 12.1b

Counts

228 → 15

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* (* 3.0 a) c))
1.6b	(/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
5.1b	(/ (* -1 (/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))
25.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log` `add-cbrt-cube`
41×	`times-frac`
33×	`*-un-lft-identity`
30×	`cbrt-undiv` `div-exp`
22×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
21×	`add-cube-cbrt`
17×	`associate-/r*`
6×	`distribute-lft-out` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`sqrt-prod`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--` `associate-/l*`
1×	`sub-neg` `rem-sqrt-square` `mul-1-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-*r/` `distribute-frac-neg` `prod-diff` `associate-/r/` `associate-/l/`

Counts

4 → 128

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
11.0ms	(/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
15.0ms	(/ (* -1 (/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (* b b) (* (* 3.0 a) c))
191.0ms	(/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))
157.0ms	(/ (* -1 (/ (* 3.0 a) (/ (+ b (sqrt (- (* b b) (* (* 3.0 a) c)))) c))) (* 3.0 a))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify137.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	796	1853
1	4969	1426
2	5001	1426

prune271.0ms

Filtered

140 candidates to 90 candidates (64.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	7	6	13
Picked	1	0	1
Done	0	1	1
Total	143	12	155

Merged error: 10.3b

Counts

155 → 12

regimes352.0ms

Accuracy

92.2% (1.6b remaining)

Error of 10.6b against oracle of 9.0b and baseline of 29.6b

bsearch211.0ms

Steps

Iters	Range	Point
9	4.136575721607635e+152	2.0850798451966124e+158	1.3291736419050374e+154
10	-6.42569108438854e-260	-2.403372424182918e-272	-1.2496717882239872e-269
9	-2.9777074523227444e+74	-9.540315001687748e+64	-2.908127150434984e+74

Iters

Range

Point

4.136575721607635e+152

2.0850798451966124e+158

1.3291736419050374e+154

-6.42569108438854e-260

-2.403372424182918e-272

-1.2496717882239872e-269

-2.9777074523227444e+74

-9.540315001687748e+64

-2.908127150434984e+74

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	38
1	51	38

end0.0ms

sample1.3s

Algorithm

intervals

Results

301.0ms	1122×	body	2560	valid
272.0ms	5735×	body	80	valid
201.0ms	913×	body	1280	valid
132.0ms	2828×	body	80	nan
88.0ms	498×	body	640	valid
33.0ms	98×	body	5120	valid
28.0ms	222×	body	320	valid
12.0ms	116×	body	160	valid

Details

sample47.0ms

simplify11.0ms

prune2.0ms

localize10.0ms

rewrite22.0ms

series212.0ms

simplify45.0ms

prune220.0ms

localize16.0ms

rewrite33.0ms

series286.0ms

simplify64.0ms

prune306.0ms

localize15.0ms

rewrite43.0ms

series428.0ms

simplify140.0ms

prune542.0ms

localize12.0ms

rewrite39.0ms

series467.0ms

simplify137.0ms

prune271.0ms

regimes352.0ms

bsearch211.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling