Details

Time bar (total: 5.4s)

sample32.0ms

Algorithm
intervals
Results
13.0ms267×body80valid
4.0ms87×body80nan

simplify14.0ms

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: 20.4b

localize117.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* (* 4.0 a) c))
1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×add-sqr-sqrt
10×fma-def add-log-exp
9×add-cube-cbrt
6×pow1 sqrt-prod
4×add-exp-log expm1-log1p-u distribute-rgt-neg-in sqrt-div add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- neg-mul-1 sub-neg flip3-+ fma-neg diff-log prod-diff neg-log flip-+
Counts
4 → 77
Calls
4 calls:
3.0ms
(- (* 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)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series265.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(- (* b b) (* (* 4.0 a) c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
70.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify135.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0264600
11046558
24657542
35001542

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize117.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
6.5b
(/ (* a c) b)
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

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))))
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
8.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
175.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
19.0ms
(/ (* a c) b)
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify54.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0476777
12207680
25001672

prune412.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize124.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.2b
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
3.6b
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
37×*-un-lft-identity
34×times-frac
30×add-exp-log
25×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r*
11×cbrt-prod
10×fma-def
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×distribute-rgt-neg-in associate-/r* unswap-sqr
4×expm1-log1p-u log1p-expm1-u distribute-lft-out--
3×distribute-lft-neg-in sqrt-prod div-inv
2×flip3-- sqrt-div 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 → 136
Calls
4 calls:
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
27.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
5.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series409.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
210.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
48.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
71.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify91.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07731510
137751315
250011269

prune646.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize128.0ms

Local error

Found 4 expressions with local error:

20.0b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
20.0b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
20.0b
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
22.6b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-div
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-prod frac-times pow1/3 associate-*r/ associate-*l/ sqrt-prod
2×sqrt-div
1×rem-sqrt-square flip3-- sqrt-pow1 pow1/2 flip--
Counts
4 → 59
Calls
4 calls:
13.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
13.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
13.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series328.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
86.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
88.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0239654
1757598
22993552
35002551

prune416.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

regimes163.0ms

Accuracy

91.3% (1.3b remaining)

Error of 8.0b against oracle of 6.7b and baseline of 21.5b

bsearch200.0ms

Steps
ItersRangePoint
8
2.1878188410446244e+107
3.8616146939177386e+111
3.264911199889295e+111
10
-2.699314103090194e+180
-2.227381996671495e+165
-2.272454186637281e+165

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06891
16891

end0.0ms

sample827.0ms

Algorithm
intervals
Results
441.0ms8700×body80valid
139.0ms2997×body80nan