Details

Time bar (total: 5.7s)

sample344.0ms

Algorithm
intervals
Results
9.0ms33×body2560valid
6.0ms186×body80valid
4.0ms28×body1280valid
2.0ms86×body80nan
2.0ms15×body640valid
1.0ms5×body5120valid
1.0ms7×body320valid
0.0ms6×body160valid

simplify34.0ms

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: 34.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b
(- (* b_2 b_2) (* a c))
1.8b
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

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:
66.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms
(- (* b_2 b_2) (* a c))
22.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
14.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
30.0ms
(- (* b_2 b_2) (* a c))
68.0ms
(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0389850
11366779
25001753

prune290.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.2b

localize14.0ms

Local error

Found 4 expressions with local error:

1.4b
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.1b
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.4b
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite192.0ms

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:
31.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
80.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
55.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
131.0ms
(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
156.0ms
(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
54.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify145.0ms

Algorithm
egg-herbie
Counts
296 → 296
Iterations

Useful iterations: 2 (101.0ms)

IterNodesCost
09195579
139184508
250014505

prune566.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

3.1b
(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
88×times-frac
55×add-sqr-sqrt
52×*-un-lft-identity
36×add-cube-cbrt
29×add-exp-log
28×cbrt-prod
20×add-cbrt-cube
16×associate-/l*
15×cbrt-undiv div-exp
13×sqrt-prod
8×cbrt-div associate-/r/ distribute-lft-out-- difference-of-squares
7×pow1 flip3-- flip--
6×sqrt-div
5×div-inv
4×expm1-log1p-u distribute-rgt-neg-in prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r*
1×frac-2neg clear-num associate-/l/
Counts
4 → 143
Calls
4 calls:
116.0ms
(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series369.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(/ (/ (* (/ a (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) (/ c (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))) (cbrt (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))) a)
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))
54.0ms
(sqrt (- (* b_2 b_2) (* a c)))
57.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify95.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
07133590
132693363
250013342

prune480.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

8.9b
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
11.6b
(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))
22.4b
(sqrt (- (* b_2 b_2) (* a c)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
12×times-frac
10×fma-neg prod-diff
8×add-log-exp
6×pow1 add-exp-log distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod add-cbrt-cube
5×difference-of-squares
4×expm1-log1p-u flip3-- sqrt-div associate-/r* flip-- log1p-expm1-u
3×associate-/l*
2×neg-mul-1 rem-sqrt-square sqrt-pow1 pow1/2 diff-log associate-/r/ associate-/l/
1×cbrt-undiv associate--l- neg-sub0 sub-neg frac-2neg flip3-+ div-exp neg-log clear-num flip-+ div-inv
Counts
4 → 108
Calls
4 calls:
14.0ms
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
31.0ms
(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))
11.0ms
(sqrt (- (* b_2 b_2) (* a c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
155.0ms
(/ (+ 0 (* a c)) (- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))))))
53.0ms
(sqrt (- (* b_2 b_2) (* a c)))
56.0ms
(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04511972
118901604
250011541

prune342.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.1b

regimes236.0ms

Accuracy

83.5% (4.4b remaining)

Error of 10.1b against oracle of 5.7b and baseline of 32.4b

bsearch98.0ms

Steps
ItersRangePoint
10
7.028227535098625e-82
3.98361551741597e-66
4.900281832529237e-79
10
-1.6375536470903724e+107
-1.9877314958440015e+97
-1.2574766781276779e+107

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03214
13214

end0.0ms

sample1.0s

Algorithm
intervals
Results
192.0ms1051×body2560valid
188.0ms5865×body80valid
136.0ms933×body1280valid
85.0ms2810×body80nan
51.0ms457×body640valid
25.0ms113×body5120valid
20.0ms232×body320valid
7.0ms120×body160valid