Details

sample244.0ms

Algorithm

intervals

Results

195.0ms	95×	body	80	nan
8.0ms	193×	body	80	valid
8.0ms	30×	body	1280	valid
7.0ms	27×	body	2560	valid
3.0ms	18×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	6×	body	160	valid
0.0ms	1×	body	5120	valid

simplify447.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune13.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.6b	(- (* b_2 b_2) (* a c))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

9.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
7.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5242	1411

prune144.0ms

Filtered

70 candidates to 96 candidates (-37.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	8	97

Merged error: 5.2b

Counts

97 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
2.9b	(/ (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.2b	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
99×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
21×	`associate-/l*`
17×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
7×	`associate-/r*`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `distribute-frac-neg` `sqrt-prod` `associate-/l/`
2×	`flip3--` `frac-2neg` `sub0-neg` `sqrt-div` `clear-num` `flip--`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 156

Calls

4 calls:

5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(/ (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
8.0ms	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
52.0ms	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify62.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5133	3744

prune190.0ms

Filtered

132 candidates to 168 candidates (-27.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	165	3	168
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	167	9	176

Merged error: 5.1b

Counts

176 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
1.6b	(- (* b_2 b_2) (* a c))
2.4b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

7.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5054	1111

prune112.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	83	10	93

Merged error: 5.0b

Counts

93 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

2.4b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
3.0b	(* (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
9.2b	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`times-frac`
29×	`add-cube-cbrt`
28×	`add-exp-log`
18×	`associate-l` `add-cbrt-cube`
13×	`associate-r`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out`
7×	`pow1`
6×	`add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`associate-/r*` `associate-/r/` `cbrt-unprod`
3×	`flip3-+` `sqrt-prod` `flip-+` `div-inv` `associate-/l*`
2×	`rec-exp` `flip3--` `sub0-neg` `sqrt-div` `1-exp` `distribute-frac-neg` `flip--` `associate-/l/`
1×	`+-commutative` `distribute-lft-neg-out` `frac-times` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `un-div-inv` `*-commutative`

Counts

4 → 127

Calls

4 calls:

5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(* (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
8.0ms	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(* (/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
53.0ms	(/ (- 0 (* a c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4922	2362
1	4922	2362

prune137.0ms

Filtered

104 candidates to 139 candidates (-33.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	140	9	149

Merged error: 5.0b

Counts

149 → 9

regimes314.0ms

Accuracy

94.6% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.4b

bsearch98.0ms

Steps

Iters	Range	Point
8	1.838480289737433e+68	1.744360026235418e+71	1.0729035470079235e+71
9	-6.695429941707738e-297	-7.676761036242019e-305	-7.883473021605369e-300
9	-6.247250655316605e+139	-3.660489123272618e+133	-3.8900654094429814e+133

Iters

Range

Point

1.838480289737433e+68

1.744360026235418e+71

1.0729035470079235e+71

-6.695429941707738e-297

-7.676761036242019e-305

-7.883473021605369e-300

-6.247250655316605e+139

-3.660489123272618e+133

-3.8900654094429814e+133

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	64
1	63	64

end0.0ms

sample1.4s

Algorithm

intervals

Results

268.0ms	1071×	body	2560	valid
257.0ms	5817×	body	80	valid
184.0ms	910×	body	1280	valid
122.0ms	2945×	body	80	nan
75.0ms	476×	body	640	valid
33.0ms	112×	body	5120	valid
25.0ms	212×	body	320	valid
10.0ms	118×	body	160	valid

Details

sample244.0ms

simplify447.0ms

prune13.0ms

localize11.0ms

rewrite38.0ms

series66.0ms

simplify52.0ms

prune144.0ms

localize11.0ms

rewrite35.0ms

series123.0ms

simplify62.0ms

prune190.0ms

localize11.0ms

rewrite23.0ms

series80.0ms

simplify43.0ms

prune112.0ms

localize15.0ms

rewrite37.0ms

series119.0ms

simplify55.0ms

prune137.0ms

regimes314.0ms

bsearch98.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling