Details

Time bar (total: 5.6s)

sample37.0ms

Algorithm
intervals
Results
14.0ms281×body80valid
4.0ms94×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03918
18018
214318
317718
418918
519318
619318

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.0b

localize91.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite229.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
58×*-un-lft-identity
56×add-sqr-sqrt
50×add-cube-cbrt
37×sqrt-prod
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
12×add-log-exp
10×fma-def fma-neg
8×neg-mul-1
6×pow1
4×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
3×flip3-- flip--
2×neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 diff-log neg-log sum-log distribute-lft-out distribute-lft-out-- difference-of-squares
1×+-commutative associate--l- associate-+l- sub-neg flip3-+ flip-+
Counts
4 → 151
Calls
4 calls:
29.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
173.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series321.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
80.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04183056
114712008
250011917

prune428.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 9.6b

localize91.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.3b
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
8.8b
(/ (* a c) b)
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
17×add-sqr-sqrt
14×add-exp-log add-cbrt-cube
12×add-cube-cbrt
10×fma-def
9×times-frac
8×add-log-exp
7×associate-/l*
6×distribute-rgt-neg-in
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp associate-/r* log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in sqrt-prod
2×flip3-- frac-2neg sqrt-div prod-exp clear-num sum-log flip-- cbrt-unprod div-inv associate-/l/ distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 div-sub neg-log flip-+
Counts
4 → 99
Calls
4 calls:
41.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
83.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
9.0ms
(/ (* a c) b)
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series252.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
64.0ms
(/ (- (- b) (- b (* 2.0 (/ (* a c) b)))) (* 2.0 a))
21.0ms
(/ (* a c) b)
79.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
0513807
12279711
25001703

prune436.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 7.3b

localize86.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite90.0ms

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-/r*
4×expm1-log1p-u log1p-expm1-u
3×distribute-lft-neg-in sqrt-prod
2×cbrt-undiv flip3-- flip3-+ sqrt-div div-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff neg-log prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 89
Calls
4 calls:
42.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
25.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series404.0ms

Counts
4 → 12
Calls
4 calls:
199.0ms
(/ (* 2.0 c) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
50.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify45.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0400830
11671721
25002704

prune374.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize89.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.0b
(- (* b b) (* (* 4.0 a) c))
1.8b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.7b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
26×add-exp-log
21×associate-*r*
18×add-sqr-sqrt
17×add-cube-cbrt
16×add-cbrt-cube
15×times-frac
12×prod-exp
10×pow1 fma-def add-log-exp
8×distribute-lft-out
7×distribute-rgt-neg-in
6×cbrt-unprod
4×expm1-log1p-u div-exp log1p-expm1-u
3×distribute-lft-neg-in pow-prod-down sqrt-prod
2×cbrt-undiv rec-exp flip3-- flip3-+ sqrt-div 1-exp sum-log associate-/r/ flip-- flip-+
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg diff-log associate-*r/ associate-*l* prod-diff neg-log un-div-inv *-commutative div-inv
Counts
4 → 108
Calls
4 calls:
77.0ms
(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms
(- (* b b) (* (* 4.0 a) c))
26.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
198.0ms
(* (* 2.0 c) (/ 1 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
47.0ms
(- (* b b) (* (* 4.0 a) c))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify65.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
05341029
12502860
25002828

prune387.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

regimes213.0ms

Accuracy

92.2% (1.1b remaining)

Error of 7.6b against oracle of 6.4b and baseline of 21.1b

bsearch295.0ms

Steps
ItersRangePoint
8
3.1248942757642245e+89
1.1714167766929137e+92
1.378005060912798e+90
10
1.2311923035801406e-286
5.850504429783805e-277
1.24767440801605e-286
10
-5.024868303916657e+156
-7.485719939656648e+141
-1.3256546684561791e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05964
15964

end0.0ms

sample896.0ms

Algorithm
intervals
Results
437.0ms8738×body80valid
127.0ms2943×body80nan