Details

Time bar (total: 6.6s)

sample36.0ms

Algorithm
intervals
Results
15.0ms280×body80valid
5.0ms112×body80nan

simplify15.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03618
16718
212318
316018
417518
517718
617718

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.0b

localize119.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

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:
16.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04183056
114712008
250011917

prune443.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.5b

localize118.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
4.4b
(/ (* a c) b)
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

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 associate-/r*
8×add-log-exp
6×distribute-rgt-neg-in
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp 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 associate-/r/ flip-- cbrt-unprod div-inv distribute-lft-out associate-/l* difference-of-squares
1×+-commutative neg-sub0 associate-+l- neg-mul-1 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 98
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series352.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
179.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
19.0ms
(/ (* a c) b)
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify57.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0476777
12207680
25001672

prune426.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.7b

localize127.0ms

Local error

Found 4 expressions with local error:

1.4b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))))))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.7b
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
62×times-frac
49×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
25×associate-*r*
22×associate-*l*
21×add-cbrt-cube
16×sqrt-prod
12×unpow-prod-down div-exp unswap-sqr
10×fma-def
9×prod-exp
8×add-log-exp
7×pow1
6×cbrt-undiv distribute-rgt-neg-in associate-/r* sqr-pow
5×cbrt-unprod
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in div-inv
2×pow-to-exp flip3-- sqrt-div pow-exp sum-log associate-/r/ flip-- distribute-lft-out difference-of-squares
1×+-commutative neg-sub0 frac-times associate-+l- neg-mul-1 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow1/2 associate-*r/ pow-prod-down neg-log associate-*l/ clear-num *-commutative flip-+ associate-/l*
Counts
4 → 160
Calls
4 calls:
20.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))))))
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series666.0ms

Counts
4 → 12
Calls
4 calls:
469.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (sqrt b)) (/ c (pow b 1/2)))))))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms
(* (/ a (sqrt b)) (/ c (pow b 1/2)))
74.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (97.0ms)

IterNodesCost
09311528
145101358
250011355

prune758.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.7b

localize132.0ms

Local error

Found 4 expressions with local error:

4.4b
(cbrt (/ c (pow b 1/2)))
4.4b
(cbrt (/ c (pow b 1/2)))
4.4b
(cbrt (/ c (pow b 1/2)))
22.0b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
75×cbrt-prod
63×times-frac
48×add-sqr-sqrt
47×add-cube-cbrt *-un-lft-identity
27×unpow-prod-down
9×sqr-pow
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod div-inv
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 125
Calls
4 calls:
3.0ms
(cbrt (/ c (pow b 1/2)))
3.0ms
(cbrt (/ c (pow b 1/2)))
3.0ms
(cbrt (/ c (pow b 1/2)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series456.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(cbrt (/ c (pow b 1/2)))
131.0ms
(cbrt (/ c (pow b 1/2)))
127.0ms
(cbrt (/ c (pow b 1/2)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03451124
111441098
250011091

prune806.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.7b

regimes192.0ms

Accuracy

93.5% (0.9b remaining)

Error of 7.7b against oracle of 6.7b and baseline of 21.1b

bsearch349.0ms

Steps
ItersRangePoint
9
2.6683347110001497e+63
3.895668027475672e+69
3.688339606012e+69
10
-2.0369510893777665e-297
3.098498077083345e-307
-1.0787310192989e-310
9
-3.6963232668708646e+158
-3.0922224130316533e+150
-1.3459740091915103e+154

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07592
17592

end0.0ms

sample857.0ms

Algorithm
intervals
Results
456.0ms8714×body80valid
136.0ms2903×body80nan