Details

Time bar (total: 5.7s)

sample285.0ms

Algorithm
intervals
Results
13.0ms194×body80valid
7.0ms30×body2560valid
5.0ms100×body80nan
5.0ms28×body1280valid
2.0ms14×body640valid
1.0ms8×body320valid
1.0ms2×body5120valid
1.0ms6×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0157
1237
2307
3327
4347
5347

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b
(- (* b_2 b_2) (* a c))
1.9b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
19×add-sqr-sqrt
18×add-cube-cbrt
15×times-frac
10×fma-def distribute-lft-out add-log-exp
8×distribute-rgt-neg-in
6×add-exp-log add-cbrt-cube
5×pow1 associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in associate-/r* sqrt-prod
2×neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div sum-log flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub div-exp prod-diff neg-log clear-num div-inv
Counts
4 → 100
Calls
4 calls:
41.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms
(- (* b_2 b_2) (* a c))
12.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series280.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms
(- (* b_2 b_2) (* a c))
71.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune315.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.7b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.8b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
199×add-sqr-sqrt
198×*-un-lft-identity
186×times-frac
130×add-cube-cbrt
60×prod-diff
50×sqrt-prod
38×distribute-rgt-neg-in
34×distribute-lft-out-- difference-of-squares
30×associate-/l*
21×distribute-lft-neg-in
11×add-exp-log add-cbrt-cube
10×fma-neg associate-/r* associate-/r/
8×add-log-exp
7×neg-mul-1 flip3-- flip--
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×associate-/l/
2×frac-2neg sqrt-div diff-log clear-num
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 284
Calls
4 calls:
18.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
26.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
147.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
170.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
09195579
139184508
250014505

prune617.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b_2 b_2) (* a c))
1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.7b
(/ a (* a c))
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
53×add-sqr-sqrt
52×*-un-lft-identity
48×add-cube-cbrt
34×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×flip3-- times-frac diff-log flip-- associate-/l*
2×cbrt-undiv sub-neg sqrt-div div-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 146
Calls
4 calls:
3.0ms
(- (* b_2 b_2) (* a c))
20.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms
(/ a (* a c))
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series179.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms
(/ a (* a c))
61.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04732541
116081646
250011557

prune292.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.4b
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.7b
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
23.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
171×add-sqr-sqrt
170×*-un-lft-identity
162×times-frac
118×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
32×add-exp-log
28×associate-/r*
26×distribute-lft-out-- difference-of-squares
23×add-cbrt-cube
21×distribute-lft-neg-in
16×div-exp
10×cbrt-undiv fma-neg
8×add-log-exp
7×neg-mul-1
6×prod-exp div-inv
5×pow1
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×1-exp cbrt-unprod
2×flip3-- frac-2neg sqrt-div diff-log clear-num flip--
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ neg-log associate-/r/ associate-/l/
Counts
4 → 258
Calls
4 calls:
16.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
28.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
20.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series473.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
185.0ms
(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
154.0ms
(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
66.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify122.0ms

Algorithm
egg-herbie
Counts
270 → 270
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
09864687
142873613
250013595

prune508.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 5.5b

regimes148.0ms

Accuracy

74.6% (6.7b remaining)

Error of 12.5b against oracle of 5.8b and baseline of 32.2b

bsearch136.0ms

Steps
ItersRangePoint
10
6.843201085887195e+41
3.4193324388629615e+53
7.998536525451512e+49
10
-2.4076762225838956e-89
-7.528955394503449e-103
-3.581294904804354e-96

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03618
13618

end0.0ms

sample1.3s

Algorithm
intervals
Results
327.0ms5937×body80valid
240.0ms1022×body2560valid
166.0ms880×body1280valid
154.0ms2905×body80nan
66.0ms435×body640valid
35.0ms116×body5120valid
30.0ms252×body320valid
9.0ms106×body160valid