Details

Time bar (total: 20.8s)

sample292.0ms

Algorithm
intervals
Results
7.0ms177×body80valid
7.0ms38×body2560valid
4.0ms26×body1280valid
3.0ms112×body80nan
2.0ms20×body640valid
1.0ms6×body5120valid
1.0ms9×body320valid
0.0ms4×body160valid

simplify13.0ms

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: 34.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b
(- (* b_2 b_2) (* a c))
1.7b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite73.0ms

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:
46.0ms
(/ (+ (- 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)))

series268.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
36.0ms
(- (* b_2 b_2) (* a c))
69.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0389850
11366779
25001753

prune304.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
5.2b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
8.8b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite114.0ms

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:
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
30.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
140.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
168.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
09195579
139184508
250014505

prune592.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.8b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
5.2b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite324.0ms

Algorithm
rewrite-expression-head
Rules
3489×times-frac
1872×add-sqr-sqrt
1871×*-un-lft-identity
1387×add-cube-cbrt
267×associate-/l*
242×distribute-lft-out-- difference-of-squares
154×sqrt-prod
142×distribute-rgt-neg-in
60×prod-diff
58×div-inv
41×add-exp-log
28×div-exp
23×add-cbrt-cube
21×distribute-lft-neg-in
13×cbrt-undiv
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1
4×expm1-log1p-u associate-/r/ log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 1226
Calls
4 calls:
20.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
111.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
89.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
106.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
63.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify279.0ms

Algorithm
egg-herbie
Counts
1238 → 1238
Iterations

Useful iterations: 1 (70.0ms)

IterNodesCost
0446326936
1500225697

prune2.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
1.0b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
22.0b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite798.0ms

Algorithm
rewrite-expression-head
Rules
11418×times-frac
5965×add-sqr-sqrt
5964×*-un-lft-identity
4352×add-cube-cbrt
2703×cbrt-prod
806×distribute-lft-out-- difference-of-squares
477×associate-/l*
436×sqrt-prod
424×distribute-rgt-neg-in
97×div-inv
60×prod-diff
41×add-exp-log
28×div-exp
21×distribute-lft-neg-in
17×add-cbrt-cube
13×cbrt-undiv
10×fma-neg
9×associate-/r*
8×add-log-exp
7×neg-mul-1 associate-/r/
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×rec-exp 1-exp
2×flip3-- frac-2neg sqrt-div diff-log div-sub clear-num flip-- associate-/l/
1×associate--l- neg-sub0 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 neg-log
Counts
4 → 3362
Calls
4 calls:
46.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
17.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
203.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
5.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)
70.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
109.0ms
(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (cbrt a)) c)) (cbrt a))
68.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify770.0ms

Algorithm
egg-herbie
Counts
3374 → 3374
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
0500194243

prune11.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.6b

regimes146.0ms

Accuracy

93.9% (1.6b remaining)

Error of 7.1b against oracle of 5.5b and baseline of 31.1b

bsearch152.0ms

Steps
ItersRangePoint
9
3.895668027475672e+69
5.84241073219057e+75
5.94192058439483e+74
6
-8.36501767772797e-260
-8.1135434350231975e-261
-9.977980439923078e-261
9
-1.2294333374423815e+100
-1.4471431684397531e+91
-4.301018409236461e+98

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05137
15137

end0.0ms

sample1.0s

Algorithm
intervals
Results
212.0ms1087×body2560valid
195.0ms5821×body80valid
144.0ms887×body1280valid
90.0ms2899×body80nan
62.0ms456×body640valid
28.0ms99×body5120valid
22.0ms241×body320valid
8.0ms123×body160valid