Details

Time bar (total: 5.3s)

sample33.0ms

Algorithm
intervals
Results
13.0ms267×body80valid
4.0ms87×body80nan

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03518
16618
211618
314418
415918
516118
616118

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.4b

localize124.0ms

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)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg distribute-rgt-neg-in flip3-+ diff-log neg-log flip-+
Counts
4 → 57
Calls
4 calls:
3.0ms
(- (* b b) (* (* 4.0 a) c))
11.0ms
(+ (- 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)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(- (* b b) (* (* 4.0 a) c))
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
72.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))
76.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify122.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (115.0ms)

IterNodesCost
0236533
1919501
23961487
35001484

prune279.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 8.2b

localize128.0ms

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)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
14×add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt times-frac associate-/r*
8×add-log-exp
5×pow1
4×cbrt-undiv div-exp distribute-lft-out--
3×distribute-rgt-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- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 80
Calls
4 calls:
11.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
3.0ms
(/ (* a c) b)
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
183.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (/ (* a c) b)))))
19.0ms
(/ (* a c) b)
73.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify51.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0454718
12113629
25001621

prune345.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

localize130.0ms

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)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
34×*-un-lft-identity times-frac
30×add-exp-log
23×add-cbrt-cube
22×add-cube-cbrt associate-*r*
11×cbrt-prod
9×cbrt-undiv div-exp prod-exp cbrt-unprod
8×add-log-exp
7×pow1 associate-*l*
6×associate-/r* unswap-sqr
4×distribute-lft-out--
3×distribute-rgt-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- 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 → 118
Calls
4 calls:
15.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
24.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
4.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series425.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
223.0ms
(/ (* 2.0 c) (- (- b) (- b (* 2.0 (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))))))
55.0ms
(* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b)))
69.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify90.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07511431
136801244
250021199

prune595.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.3b

localize137.0ms

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 add-cbrt-cube 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 → 51
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)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
91.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
93.0ms
(cbrt (* (/ a (* (cbrt b) (cbrt b))) (/ c (cbrt b))))
75.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify82.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0227588
1714532
22768486
35001485

prune396.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.3b

regimes172.0ms

Accuracy

91.3% (1.3b remaining)

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

bsearch204.0ms

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
06771
16771

end0.0ms

sample833.0ms

Algorithm
intervals
Results
439.0ms8700×body80valid
140.0ms2997×body80nan