Details

sample307.0ms

Algorithm

intervals

Results

14.0ms	42×	body	2560	valid
12.0ms	186×	body	80	valid
6.0ms	23×	body	1280	valid
5.0ms	79×	body	80	nan
3.0ms	14×	body	640	valid
3.0ms	8×	body	160	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	5120	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	33	7
2	46	7
3	49	7
4	49	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

47.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	549	3055
1	1826	2150
2	5002	2063

prune359.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`add-exp-log` `associate-r`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

59.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
38.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify77.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	609	2985
1	2334	1993
2	5002	1940

prune328.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.5b

localize4.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify6.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	0	0

prune10.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.5b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 2 (/ b_2 a))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 34

Calls

1 calls:

9.0ms

(* 2 (/ b_2 a))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 2 (/ b_2 a))

simplify67.0ms

Algorithm

egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	166	134
1	730	124
2	2975	124
3	5002	124

prune72.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 5.5b

regimes154.0ms

Accuracy

83.8% (4.6b remaining)

Error of 10.4b against oracle of 5.7b and baseline of 34.4b

bsearch116.0ms

Steps

Iters	Range		Point
9	1.0966316111626227e+109	8.247031634266059e+117	3.669945833512195e+117
9	-4.966762827316324e-118	-1.3701001010226256e-126	-4.1515494582665793e-119

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	15
1	34	15

end0.0ms

sample1.6s

Algorithm

intervals

Results

387.0ms	5878×	body	80	valid
349.0ms	1067×	body	2560	valid
250.0ms	893×	body	1280	valid
178.0ms	2986×	body	80	nan
97.0ms	445×	body	640	valid
47.0ms	116×	body	5120	valid
36.0ms	223×	body	320	valid
13.0ms	114×	body	160	valid