Details

sample289.0ms

Algorithm

intervals

Results

10.0ms	180×	body	80	valid
9.0ms	39×	body	2560	valid
7.0ms	35×	body	1280	valid
4.0ms	98×	body	80	nan
2.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
0.0ms	2×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

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: 33.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
73.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune226.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	10	93

Merged error: 5.3b

Counts

93 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
3.4b	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.4b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `associate-/r/`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 200

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
139.0ms	(/ (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	729	3368
1	3283	3193
2	5001	3167

prune440.0ms

Filtered

212 candidates to 142 candidates (67.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	214	8	222

Merged error: 5.3b

Counts

222 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
3.2b	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.4b	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 485

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
26.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
184.0ms	(/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
154.0ms	(/ (/ a (/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

497 → 497

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1536	8629
1	5001	7982

prune919.0ms

Filtered

497 candidates to 298 candidates (60.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	496	1	497
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	497	8	505

Merged error: 5.3b

Counts

505 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
3.4b	(* (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
8.4b	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

81×	`add-sqr-sqrt`
65×	`*-un-lft-identity`
58×	`times-frac`
35×	`add-cube-cbrt`
28×	`add-exp-log`
27×	`associate-l`
18×	`add-cbrt-cube`
14×	`distribute-lft-out--` `difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp`
7×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
6×	`add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 145

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(* (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
12.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series406.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
143.0ms	(* (/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 a))
168.0ms	(/ (+ 0 (* a c)) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (93.0ms)

Iter	Nodes	Cost
0	700	1931
1	3287	1713
2	5002	1695

prune308.0ms

Filtered

157 candidates to 107 candidates (68.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	157	8	165

Merged error: 5.3b

Counts

165 → 8

regimes196.0ms

Accuracy

88.3% (3.1b remaining)

Error of 8.8b against oracle of 5.7b and baseline of 32.3b

bsearch136.0ms

Steps

Iters	Range	Point
9	1.7907836249739894e-10	2.3719878869137505e-05	1.224355625902438e-06
6	1.1096606956371057e-163	1.7730455537046296e-162	1.4606396673226078e-162
7	-3.394702059408153e+117	-4.3501158911079625e+115	-3.631154114249338e+116

Iters

Range

Point

1.7907836249739894e-10

2.3719878869137505e-05

1.224355625902438e-06

1.1096606956371057e-163

1.7730455537046296e-162

1.4606396673226078e-162

-3.394702059408153e+117

-4.3501158911079625e+115

-3.631154114249338e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	46	26
2	46	26

end0.0ms

sample1.2s

Algorithm

intervals

Results

270.0ms	1059×	body	2560	valid
260.0ms	5922×	body	80	valid
179.0ms	870×	body	1280	valid
125.0ms	2897×	body	80	nan
75.0ms	438×	body	640	valid
34.0ms	112×	body	5120	valid
28.0ms	234×	body	320	valid
8.0ms	103×	body	160	valid

Details

sample289.0ms

simplify15.0ms

prune4.0ms

localize12.0ms

rewrite45.0ms

series276.0ms

simplify42.0ms

prune226.0ms

localize15.0ms

rewrite46.0ms

series409.0ms

simplify114.0ms

prune440.0ms

localize11.0ms

rewrite86.0ms

series436.0ms

simplify109.0ms

prune919.0ms

localize12.0ms

rewrite45.0ms

series406.0ms

simplify110.0ms

prune308.0ms

regimes196.0ms

bsearch136.0ms

simplify2.0ms

end0.0ms

sample1.2s

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