Details

Time bar (total: 4.2s)

sample37.0ms

Algorithm
intervals
Results
7.0ms35×body2560valid
7.0ms198×body80valid
4.0ms24×body1280valid
3.0ms92×body80nan
2.0ms15×body640valid
1.0ms2×body5120valid
0.0ms5×body320valid
0.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
10×add-log-exp
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
6×distribute-lft-out
5×pow1 times-frac associate-/l*
3×distribute-rgt-neg-in sqrt-prod
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 70
Calls
4 calls:
35.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series303.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
47.0ms
(- (* b b) (* (* 3.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0400780
11529686
25002675

prune222.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* 3.0 a) c)
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 *-un-lft-identity add-log-exp
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt
3×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
2×flip3-- sqrt-div sum-log flip-- distribute-lft-out
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square distribute-rgt-neg-in sqrt-pow1 flip3-+ pow1/2 diff-log associate-*l* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
7.0ms
(* (* 3.0 a) c)
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series217.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(* (* 3.0 a) c)
79.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms
(- (* b b) (* (* 3.0 a) c))
71.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify44.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0307469
11303428
25001417

prune183.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
21×add-cube-cbrt
19×associate-*r*
16×add-cbrt-cube
13×associate-*l*
10×add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1
6×unswap-sqr
4×cbrt-undiv distribute-rgt-neg-in cbrt-unprod
3×sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+l- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down neg-log associate-*l/ *-commutative flip-+
Counts
4 → 104
Calls
4 calls:
57.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
14.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series311.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(* (/ 1 3.0) (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) a))
81.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms
(- (* b b) (* (* 3.0 a) c))
74.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify70.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
06121234
129861078
250011068

prune272.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
0.9b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b
(- (* b b) (* (* 3.0 a) c))
23.0b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt *-un-lft-identity
31×times-frac
26×add-exp-log
21×add-cube-cbrt
19×associate-*l*
16×add-cbrt-cube
13×associate-*r*
10×add-log-exp
8×div-exp prod-exp distribute-lft-out
7×pow1
6×unswap-sqr
4×cbrt-undiv distribute-rgt-neg-in cbrt-unprod
3×sqrt-prod
2×rec-exp flip3-- sqrt-div 1-exp sum-log flip-- div-inv
1×+-commutative neg-sub0 frac-times associate-+l- sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r/ pow-prod-down neg-log associate-*l/ un-div-inv *-commutative flip-+
Counts
4 → 105
Calls
4 calls:
59.0ms
(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
12.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms
(- (* b b) (* (* 3.0 a) c))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series299.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) 3.0) (/ 1 a))
76.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms
(- (* b b) (* (* 3.0 a) c))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify66.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
06111270
126111118
250021101

prune248.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.8b

regimes374.0ms

Accuracy

84.8% (4.4b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 34.6b

bsearch108.0ms

Steps
ItersRangePoint
9
3.6106127752583374e-71
6.7695755698382385e-65
9.390367471089922e-69
9
-8.652530131639494e+154
-2.4576771469086066e+149
-6.795865910643866e+150

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03316
13316

end0.0ms

sample1.1s

Algorithm
intervals
Results
234.0ms1113×body2560valid
206.0ms5729×body80valid
161.0ms931×body1280valid
95.0ms2854×body80nan
66.0ms471×body640valid
26.0ms101×body5120valid
24.0ms244×body320valid
9.0ms109×body160valid