Details

Time bar (total: 6.7s)

sample55.0ms

Algorithm
intervals
Results
13.0ms146×body160valid
9.0ms530×pre80true
9.0ms274×body80nan
4.0ms110×body80valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0259
1469
2869
31139
41219
51219

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
29.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
11×add-sqr-sqrt
10×add-cube-cbrt fma-def add-log-exp
9×add-exp-log add-cbrt-cube
6×distribute-rgt-neg-in distribute-lft-out
5×pow1 times-frac associate-/l*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log div-sub prod-diff neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 90
Calls
4 calls:
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
10.0ms
(- (* b b) (* (* 4.0 a) c))
64.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
21.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series311.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
45.0ms
(- (* b b) (* (* 4.0 a) c))
108.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0438854
11702750
25002735

prune250.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite184.0ms

Algorithm
rewrite-expression-head
Rules
123×add-sqr-sqrt *-un-lft-identity
90×times-frac
79×add-cube-cbrt
61×prod-diff
41×sqrt-prod
32×distribute-rgt-neg-in
30×associate-/l*
22×distribute-lft-out-- difference-of-squares
21×distribute-lft-neg-in
18×add-exp-log add-cbrt-cube
11×fma-neg
10×add-log-exp
8×associate-/r*
7×cbrt-undiv neg-mul-1 div-exp
6×associate-/r/
5×flip3-- flip--
4×pow1 expm1-log1p-u log1p-expm1-u div-inv
3×diff-log associate-/l/
2×sub-neg frac-2neg prod-exp clear-num cbrt-unprod
1×associate--l- neg-sub0 flip3-+ neg-log flip-+
Counts
4 → 231
Calls
4 calls:
28.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
80.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
57.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series467.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
149.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
188.0ms
(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify148.0ms

Algorithm
egg-herbie
Counts
243 → 243
Iterations

Useful iterations: 2 (115.0ms)

IterNodesCost
08325099
139673830
250013828

prune542.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- (* (- (sqrt b)) (sqrt b)) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- 1) 1)))) (* 2.0 a))
0.3b
(/ (+ 0 (* 4.0 (* a c))) (+ (- (* (- (sqrt b)) (sqrt b)) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- 1) 1))))
0.5b
(* (- (sqrt b)) (sqrt b))

rewrite388.0ms

Algorithm
rewrite-expression-head
Rules
58×times-frac
54×associate-/r/
48×frac-add
43×flip3-- flip--
37×add-sqr-sqrt
36×sqrt-div
34×associate-/l*
33×add-cube-cbrt *-un-lft-identity
24×frac-times
22×flip3-+ flip-+
20×add-exp-log add-cbrt-cube
16×associate-*l*
12×associate-*r/ associate-*l/
10×sqrt-prod
7×cbrt-undiv div-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in associate-*r* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
3×prod-exp cbrt-unprod associate-/l/
2×frac-2neg clear-num unswap-sqr
1×distribute-lft-neg-out neg-mul-1 sub-neg fma-neg diff-log prod-diff pow-prod-down *-commutative
Counts
4 → 187
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
217.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- (* (- (sqrt b)) (sqrt b)) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- 1) 1)))) (* 2.0 a))
136.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (- (* (- (sqrt b)) (sqrt b)) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- 1) 1))))
17.0ms
(* (- (sqrt b)) (sqrt b))

series473.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
182.0ms
(/ (/ (+ 0 (* 4.0 (* a c))) (+ (- (* (- (sqrt b)) (sqrt b)) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- 1) 1)))) (* 2.0 a))
214.0ms
(/ (+ 0 (* 4.0 (* a c))) (+ (- (* (- (sqrt b)) (sqrt b)) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (sqrt (- (* b b) (* (* 4.0 a) c))) (+ (- 1) 1))))
31.0ms
(* (- (sqrt b)) (sqrt b))

simplify79.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
012816416
150015489

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.3b
(/ (* 2.0 a) (* 4.0 (* a c)))
0.3b
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (fma -1 b (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.4b
(* (/ (* 2.0 a) (* 4.0 (* a c))) (fma -1 b (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

rewrite188.0ms

Algorithm
rewrite-expression-head
Rules
152×add-exp-log
92×add-cbrt-cube
73×prod-exp
46×div-exp
41×cbrt-unprod
26×cbrt-undiv
10×add-sqr-sqrt
9×pow1
8×add-cube-cbrt rec-exp *-un-lft-identity 1-exp
6×add-log-exp
5×times-frac associate-*l*
4×expm1-log1p-u log1p-expm1-u associate-/l*
3×associate-*r* div-inv
2×pow-flip frac-2neg pow-prod-down associate-*l/ clear-num associate-/r* fma-udef
1×distribute-rgt-in sub-neg flip3-- distribute-lft-in fma-neg diff-log prod-diff associate-/r/ *-commutative flip-- inv-pow unswap-sqr
Counts
4 → 135
Calls
4 calls:
8.0ms
(- (* b b) (* (* 4.0 a) c))
20.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
93.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (fma -1 b (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
60.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (fma -1 b (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

series325.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
12.0ms
(/ (* 2.0 a) (* 4.0 (* a c)))
171.0ms
(/ 1 (* (/ (* 2.0 a) (* 4.0 (* a c))) (fma -1 b (- (sqrt (- (* b b) (* (* 4.0 a) c)))))))
98.0ms
(* (/ (* 2.0 a) (* 4.0 (* a c))) (fma -1 b (- (sqrt (- (* b b) (* (* 4.0 a) c))))))

simplify115.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 2 (100.0ms)

IterNodesCost
07312000
145651479
250011460

prune273.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02717
12717

end0.0ms

sample1.4s

Algorithm
intervals
Results
295.0ms4459×body160valid
283.0ms8761×body80nan
278.0ms16761×pre80true
124.0ms3541×body80valid