Details

Time bar (total: 4.6s)

sample39.0ms

Algorithm
intervals
Results
7.0ms31×body2560valid
7.0ms178×body80valid
4.0ms22×body1280valid
3.0ms23×body640valid
3.0ms89×body80nan
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms3×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0289
1649
21149
31359
41449
51489
61489

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
20.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×add-cube-cbrt times-frac associate-/l*
6×sqrt-prod distribute-lft-out-- difference-of-squares
5×pow1
4×flip3-- flip--
3×distribute-rgt-neg-in diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 77
Calls
4 calls:
33.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
16.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
78.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0404890
11481801
25001796

prune434.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.5b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.8b
(- (* b b) (* 4.0 (* a c)))
20.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
19×add-sqr-sqrt
16×*-un-lft-identity
13×add-cbrt-cube
10×prod-exp add-log-exp
8×add-cube-cbrt
7×pow1 associate-*r* associate-*l*
5×flip3-- sqrt-prod flip--
4×div-exp cbrt-unprod distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp distribute-rgt-neg-in sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 85
Calls
4 calls:
55.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
12.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series283.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
76.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify60.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0469991
12048866
25002857

prune231.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
0.8b
(- (* b b) (* 4.0 (* a c)))
6.4b
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
20.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
15×*-un-lft-identity
12×add-sqr-sqrt
10×times-frac
9×add-exp-log add-cube-cbrt sqrt-prod add-cbrt-cube
8×add-log-exp
6×associate-/l*
5×pow1
4×flip3-- sqrt-div flip--
3×div-inv distribute-lft-out--
2×cbrt-undiv sub-neg diff-log div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square distribute-rgt-out-- distribute-rgt-neg-in frac-2neg sqrt-pow1 pow1/2 div-sub prod-exp clear-num associate-/r* frac-sub cbrt-unprod sub-div difference-of-squares
Counts
4 → 76
Calls
4 calls:
8.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
3.0ms
(- (* b b) (* 4.0 (* a c)))
26.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series344.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a))
47.0ms
(- (* b b) (* 4.0 (* a c)))
105.0ms
(- (/ (- b) (* 2.0 a)) (/ (sqrt (- (* b b) (* 4.0 (* a c)))) (* 2.0 a)))
70.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0419882
11458817
25001806

prune247.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b
(- (* b b) (* 4.0 (* a c)))
13.5b
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
16.1b
(- (pow b 2) (pow b 2))
20.8b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
23×add-exp-log
22×unpow-prod-down
20×*-un-lft-identity
16×add-cube-cbrt difference-of-squares
13×add-cbrt-cube
12×unpow2 sqr-pow
10×distribute-rgt-out-- prod-exp
8×distribute-lft-out-- add-log-exp
7×pow1 associate-*l*
4×div-exp cbrt-unprod
3×flip3-- times-frac associate-*r* sqrt-prod flip--
2×cbrt-undiv frac-times sub-neg rec-exp flip3-+ sqrt-div diff-log 1-exp associate-*r/ flip-+
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 +-inverses pow-prod-down associate-*l/ *-commutative div-inv unswap-sqr
Counts
4 → 111
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
181.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
11.0ms
(- (pow b 2) (pow b 2))
4.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(- (* b b) (* 4.0 (* a c)))
12.0ms
(* (/ 1 (* 2.0 a)) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))))
1.0ms
(- (pow b 2) (pow b 2))
72.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify324.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (314.0ms)

IterNodesCost
0591781
14612569
25001561

prune278.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.0b

regimes141.0ms

Accuracy

93.9% (1.5b remaining)

Error of 7.2b against oracle of 5.7b and baseline of 30.3b

bsearch142.0ms

Steps
ItersRangePoint
4
1.4117953071395708e+85
2.422703580179915e+85
1.5018928133646766e+85
8
-4.972658484620048e-292
-3.4579621013844897e-295
-3.497999691431546e-295
8
-6.6886088143369254e+38
-2.2615366197350152e+35
-6.6114837319571935e+38

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04326
14326

end0.0ms

sample1.1s

Algorithm
intervals
Results
244.0ms1057×body2560valid
224.0ms5889×body80valid
166.0ms862×body1280valid
102.0ms2791×body80nan
72.0ms466×body640valid
28.0ms102×body5120valid
27.0ms230×body320valid
8.0ms106×body160valid