Details

Time bar (total: 6.0s)

sample63.0ms

Algorithm
intervals
Results
17.0ms201×body80valid
8.0ms21×body2560valid
8.0ms23×body1280valid
7.0ms87×body80nan
5.0ms20×body640valid
2.0ms5×body5120valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0299
1659
21219
31519
41609
51649
61649

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
61×add-sqr-sqrt prod-diff
60×*-un-lft-identity
48×add-cube-cbrt
36×sqrt-prod
24×distribute-rgt-neg-in
21×distribute-lft-neg-in
11×fma-neg
10×add-log-exp
9×add-exp-log add-cbrt-cube
7×neg-mul-1 times-frac associate-/l*
6×distribute-lft-out-- difference-of-squares
5×pow1
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-sub neg-log prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 157
Calls
4 calls:
45.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series297.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
80.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
50.0ms
(- (* b b) (* 4.0 (* a c)))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05903305
121012212
250022128

prune363.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
0.7b
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.0b
(- (* b b) (* 4.0 (* a c)))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
61×prod-diff
60×add-sqr-sqrt
57×*-un-lft-identity
49×add-cube-cbrt
35×sqrt-prod
23×add-exp-log distribute-rgt-neg-in
21×distribute-lft-neg-in
13×add-cbrt-cube
11×fma-neg
10×prod-exp add-log-exp
7×pow1 neg-mul-1 associate-*r* associate-*l*
5×flip3-- flip--
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u distribute-lft-out-- difference-of-squares
3×times-frac diff-log
2×cbrt-undiv frac-times sub-neg rec-exp sqrt-div 1-exp associate-*l/
1×associate--l- neg-sub0 rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ pow-prod-down neg-log un-div-inv *-commutative div-inv unswap-sqr
Counts
4 → 165
Calls
4 calls:
60.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
18.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms
(- (* b b) (* 4.0 (* a c)))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series298.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* 2.0 a)))
79.0ms
(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms
(- (* b b) (* 4.0 (* a c)))
76.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify85.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
06563423
125942238
250012193

prune353.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b
(- (* b b) (* 4.0 (* a c)))
8.5b
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity
11×fma-neg prod-diff
10×add-log-exp
6×pow1 distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
4×add-exp-log expm1-log1p-u flip3-- sqrt-div add-cbrt-cube flip-- log1p-expm1-u
3×diff-log
2×neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2
1×associate--l- neg-sub0 neg-log difference-of-squares
Counts
4 → 87
Calls
4 calls:
3.0ms
(- (* b b) (* 4.0 (* a c)))
8.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(- (* b b) (* 4.0 (* a c)))
80.0ms
(- (- b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
75.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))
69.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03131367
111391090
250011064

prune367.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 8.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- b))
1.0b
(- (* b b) (* 4.0 (* a c)))
19.4b
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
23.2b
(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×cbrt-prod
9×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×add-log-exp
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×distribute-lft-neg-in distribute-rgt-neg-in sqrt-prod
2×flip3-- sqrt-div flip--
1×neg-mul-1 sub-neg rem-sqrt-square sqrt-pow1 pow1/2 fma-neg pow1/3 diff-log prod-diff fma-udef
Counts
4 → 63
Calls
4 calls:
1.0ms
(cbrt (- b))
3.0ms
(- (* b b) (* 4.0 (* a c)))
0.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
5.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(cbrt (- b))
49.0ms
(- (* b b) (* 4.0 (* a c)))
353.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (sqrt (- (* b b) (* 4.0 (* a c))))))
74.0ms
(sqrt (- (* b b) (* 4.0 (* a c))))

simplify100.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 3 (93.0ms)

IterNodesCost
0249568
1776512
23355496
35001491

prune264.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 8.2b

regimes244.0ms

Accuracy

81.9% (5.2b remaining)

Error of 11.2b against oracle of 6.0b and baseline of 34.7b

bsearch148.0ms

Steps
ItersRangePoint
7
6.184155830638016e+27
1.3306260697673677e+30
1.2919983862558445e+30
9
-7.983923007473122e-12
-3.7260100270962394e-17
-3.774134686283342e-17

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03522
13522

end0.0ms

sample2.0s

Algorithm
intervals
Results
503.0ms5870×body80valid
438.0ms1038×body2560valid
315.0ms900×body1280valid
237.0ms2910×body80nan
119.0ms434×body640valid
58.0ms260×body320valid
57.0ms115×body5120valid
18.0ms127×body160valid