Details

Time bar (total: 4.1s)

sample36.0ms

Algorithm
intervals
Results
7.0ms201×body80valid
5.0ms31×body1280valid
4.0ms21×body2560valid
3.0ms103×body80nan
2.0ms13×body640valid
1.0ms3×body5120valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0219
1429
2769
3949
41029
51029

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* 3.0 a) c)
1.0b
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.2b
(- (* b b) (* (* 3.0 a) c))
19.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite28.0ms

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:
6.0ms
(* (* 3.0 a) c)
13.0ms
(+ (- 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)))

series207.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(* (* 3.0 a) c)
77.0ms
(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
45.0ms
(- (* b b) (* (* 3.0 a) c))
65.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify43.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0307469
11303428
25001417

prune190.0ms

Filtered
72 candidates to 52 candidates (72.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3.0 (* a c))
1.0b
(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
1.2b
(- (* b b) (* 3.0 (* a c)))
19.5b
(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite24.0ms

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-*l* 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-*r* neg-log *-commutative flip-+
Counts
4 → 60
Calls
4 calls:
6.0ms
(* 3.0 (* a c))
11.0ms
(+ (- 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))))

series210.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* 3.0 (* a c))
78.0ms
(+ (- b) (sqrt (- (* b b) (* 3.0 (* a c)))))
42.0ms
(- (* b b) (* 3.0 (* a c)))
68.0ms
(sqrt (- (* b b) (* 3.0 (* a c))))

simplify133.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (127.0ms)

IterNodesCost
0296468
11081427
24610415
35001414

prune173.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 10.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b
(- (* b b) (* (* 3.0 a) c))
11.0b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
19.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))
19.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log sqrt-div add-cbrt-cube
3×flip3-- flip--
2×rem-sqrt-square sqrt-pow1 pow1/2 sum-log
1×+-commutative neg-sub0 associate-+l- sub-neg flip3-+ diff-log neg-log flip-+
Counts
4 → 55
Calls
4 calls:
2.0ms
(- (* b b) (* (* 3.0 a) c))
5.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

series259.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(- (* b b) (* (* 3.0 a) c))
77.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
70.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify138.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (131.0ms)

IterNodesCost
0251648
11020537
24512523
35002521

prune223.0ms

Filtered
67 candidates to 53 candidates (79.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 10.6b

localize22.0ms

Local error

Found 4 expressions with local error:

11.0b
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
19.5b
(sqrt (- (* b b) (* (* 3.0 a) c)))
20.3b
(cbrt (- (* b b) (* (* 3.0 a) c)))
20.3b
(cbrt (- (* b b) (* (* 3.0 a) c)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt add-log-exp
7×add-cube-cbrt *-un-lft-identity
6×cbrt-prod
5×pow1
4×add-exp-log cbrt-div add-cbrt-cube
3×flip3-- sqrt-prod flip--
2×pow1/3 sqrt-div sum-log
1×+-commutative neg-sub0 associate-+l- rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 neg-log flip-+
Counts
4 → 54
Calls
4 calls:
5.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
4.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
2.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
3.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

series351.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(+ (- b) (* (sqrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c))))))))
69.0ms
(sqrt (- (* b b) (* (* 3.0 a) c)))
93.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))
94.0ms
(cbrt (- (* b b) (* (* 3.0 a) c)))

simplify138.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0330962
11206852
24939841
35001841

prune301.0ms

Filtered
66 candidates to 59 candidates (89.4%)
Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 10.6b

regimes406.0ms

Accuracy

95.5% (1.0b remaining)

Error of 13.5b against oracle of 12.5b and baseline of 34.1b

bsearch116.0ms

Steps
ItersRangePoint
7
1.4883044572870273e+152
8.269463047302798e+153
1.8041467096464137e+153
6
-5.268059566527501e-270
-4.640407349006837e-271
-8.733700690697086e-271
4
-2.4628825350256635e+163
-1.5405955983178716e+163
-1.5694170650899903e+163

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04835
15035
25035

end0.0ms

sample1.1s

Algorithm
intervals
Results
235.0ms1100×body2560valid
212.0ms5848×body80valid
161.0ms920×body1280valid
96.0ms2886×body80nan
60.0ms452×body640valid
27.0ms103×body5120valid
23.0ms228×body320valid
8.0ms122×body160valid