Details

sample74.0ms

Algorithm

intervals

Results

16.0ms	209×	body	80	valid
13.0ms	25×	body	2560	valid
11.0ms	31×	body	1280	valid
7.0ms	103×	body	80	nan
4.0ms	15×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 28.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite46.0ms

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:

19.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
6.0ms	(- (* b b) (* 4.0 (* a c)))
13.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series295.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
44.0ms	(- (* b b) (* 4.0 (* a c)))
75.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	403	779
1	1514	685
2	5002	674

prune222.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 3.6b

Counts

83 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
6.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series327.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
43.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
69.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	521	1588
1	2522	1375
2	5002	1308

prune249.0ms

Filtered

126 candidates to 71 candidates (56.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	121	5	126
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	125	9	134

Merged error: 3.5b

Counts

134 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.5b	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
17.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

333×	`times-frac`
221×	`*-un-lft-identity`
122×	`add-sqr-sqrt`
121×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out`
31×	`div-inv`
25×	`distribute-rgt-neg-in` `add-cbrt-cube`
21×	`associate-/r*`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
10×	`add-log-exp`
9×	`flip3-+` `flip-+`
7×	`associate-/l*`
5×	`pow1`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 263

Calls

4 calls:

19.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
46.0ms	(- (* b b) (* 4.0 (* a c)))
77.0ms	(+ (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1107	4693
1	5002	4134

prune383.0ms

Filtered

275 candidates to 115 candidates (41.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	274	1	275
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	275	9	284

Merged error: 3.5b

Counts

284 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ 1 (* 2.0 a)))
0.5b	(cbrt (/ 1 (* 2.0 a)))
0.5b	(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
17.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

50×	`cbrt-prod`
30×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
21×	`add-cube-cbrt`
18×	`times-frac`
12×	`pow1` `swap-sqr`
10×	`associate-r` `associate-l`
8×	`pow1/3` `div-inv`
6×	`add-exp-log` `cbrt-div`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`sqrt-div` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow-plus` `pow1/2` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 104

Calls

4 calls:

3.0ms	(cbrt (/ 1 (* 2.0 a)))
3.0ms	(cbrt (/ 1 (* 2.0 a)))
9.0ms	(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series694.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (/ 1 (* 2.0 a)))
198.0ms	(cbrt (/ 1 (* 2.0 a)))
230.0ms	(* (cbrt (/ 1 (* 2.0 a))) (cbrt (/ 1 (* 2.0 a))))
70.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify145.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	274	840
1	1033	772
2	4954	678
3	5001	678

prune309.0ms

Filtered

116 candidates to 77 candidates (66.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	116	9	125

Merged error: 3.5b

Counts

125 → 9

regimes185.0ms

Accuracy

89% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 33.9b

bsearch191.0ms

Steps

Iters	Range	Point
9	1.7536266209730185e+54	9.156208036690931e+61	3.7405136229447617e+55
9	-4.593581389442884e-257	-3.786974856544585e-264	-3.8324699600337675e-264
4	-2.2709498629311444e+153	-1.3123487377944479e+153	-1.5396067403637575e+153

Iters

Range

Point

1.7536266209730185e+54

9.156208036690931e+61

3.7405136229447617e+55

-4.593581389442884e-257

-3.786974856544585e-264

-3.8324699600337675e-264

-2.2709498629311444e+153

-1.3123487377944479e+153

-1.5396067403637575e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	32
1	48	32

end0.0ms

sample1.4s

Algorithm

intervals

Results

304.0ms	5872×	body	80	valid
300.0ms	1051×	body	2560	valid
220.0ms	896×	body	1280	valid
143.0ms	2929×	body	80	nan
85.0ms	461×	body	640	valid
37.0ms	105×	body	5120	valid
30.0ms	216×	body	320	valid
10.0ms	107×	body	160	valid