Details

Time bar (total: 2.2m)

sample156.0ms

Algorithm
intervals
Results
35.0ms193×body80valid
34.0ms29×body1280valid
31.0ms29×body2560valid
17.0ms104×body80nan
8.0ms11×body640valid
3.0ms6×body320valid
3.0ms2×body5120valid
1.0ms2×body160valid

simplify272.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
272.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize26.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma (* a c) -4 (* b b)))
1.4b
(fma (* a c) -4 (* b b))
0.7b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
60×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
10×fma-neg distribute-lft-out-- difference-of-squares
8×add-log-exp
7×neg-mul-1 associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- diff-log flip-- associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log fma-udef div-inv
Counts
4 → 167
Calls
4 calls:
Slowest
45.0ms
(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
27.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series422.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
112.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
101.0ms
(sqrt (fma (* a c) -4 (* b b)))
92.0ms
(fma (* a c) -4 (* b b))

simplify17.1s

Counts
205 → 179
Calls
205 calls:
Slowest
453.0ms
(/ (* (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (* (* 2 2) 2))
341.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))
273.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
248.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
241.0ms
(fma (* (cbrt b) (cbrt b)) (- (cbrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.8b

localize23.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma (* a c) -4 (* b b)))
1.4b
(fma (* a c) -4 (* b b))
0.7b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.2b
(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
79×add-sqr-sqrt
78×*-un-lft-identity
60×prod-diff
58×add-cube-cbrt
38×sqrt-prod
26×distribute-rgt-neg-in
21×distribute-lft-neg-in times-frac
10×fma-neg distribute-lft-out-- difference-of-squares
8×add-log-exp
7×neg-mul-1 associate-/l*
6×add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/r*
2×flip3-- diff-log flip-- associate-/l/
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 div-sub div-exp neg-log fma-udef div-inv
Counts
4 → 167
Calls
4 calls:
Slowest
22.0ms
(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
16.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series349.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
103.0ms
(/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2)
89.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
84.0ms
(sqrt (fma (* a c) -4 (* b b)))
72.0ms
(fma (* a c) -4 (* b b))

simplify17.8s

Counts
205 → 179
Calls
205 calls:
Slowest
506.0ms
(fma (- (sqrt (fma (* a c) -4 (* b b)))) 1 (* (sqrt (fma (* a c) -4 (* b b))) 1))
470.0ms
(/ (* (* (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (* (* 2 2) 2))
323.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))
269.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
249.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.8b

localize46.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma (* a c) -4 (* b b)))
1.4b
(fma (* a c) -4 (* b b))
0.7b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.5b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) (sqrt 2))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
570×times-frac
460×add-sqr-sqrt
459×*-un-lft-identity
364×sqrt-prod
287×add-cube-cbrt
86×distribute-lft-out-- difference-of-squares
64×distribute-rgt-neg-in
60×prod-diff
46×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×div-inv add-log-exp
7×neg-mul-1
6×associate-/r*
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp
2×diff-log div-sub
1×associate--l- neg-sub0 rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 neg-log fma-udef flip-- associate-/l/
Counts
4 → 465
Calls
4 calls:
Slowest
52.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) (sqrt 2))
21.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
3.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series569.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
269.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) (sqrt 2))
124.0ms
(sqrt (fma (* a c) -4 (* b b)))
102.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
74.0ms
(fma (* a c) -4 (* b b))

simplify1.2m

Counts
761 → 477
Calls
761 calls:
Slowest
550.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
273.0ms
(fma (sqrt (- b)) (sqrt (- b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
267.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
266.0ms
(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (- (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (* (cbrt (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt (fma (* a c) -4 (* b b))))))))
265.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (sqrt (* (cbrt 2) (cbrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

prune6.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.8b

localize55.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma (* a c) -4 (* b b)))
1.4b
(fma (* a c) -4 (* b b))
1.0b
(/ (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
1.0b
(/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
96×times-frac
75×sqrt-prod
52×add-sqr-sqrt
51×*-un-lft-identity add-cube-cbrt
34×add-exp-log
15×pow1 div-exp
14×add-cbrt-cube pow1/3
13×pow-flip
12×div-inv
10×associate-/r* associate-/l*
7×cbrt-undiv
6×prod-exp
4×expm1-log1p-u rec-exp 1-exp pow-sqr pow-prod-up insert-posit16 log1p-expm1-u add-log-exp pow-div
3×sqrt-pow1 pow1/2
2×clear-num frac-2neg pow-prod-down cbrt-unprod
1×pow2 rem-sqrt-square pow-plus fma-udef inv-pow associate-/l/
Counts
4 → 172
Calls
4 calls:
Slowest
23.0ms
(/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
20.0ms
(/ (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series187.0ms

Counts
4 → 8
Calls
4 calls:
Slowest
100.0ms
(sqrt (fma (* a c) -4 (* b b)))
87.0ms
(fma (* a c) -4 (* b b))
0.0ms
(/ (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (sqrt (sqrt 2)))
0.0ms
(/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))

simplify8.8s

Counts
197 → 180
Calls
197 calls:
Slowest
875.0ms
(/ (* (* (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
449.0ms
(/ (/ (* (* 1 1) 1) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
430.0ms
(/ (* (cbrt (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (cbrt (/ 1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))) (sqrt (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
426.0ms
(/ (* (* 1 1) 1) (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))))
188.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (cbrt (sqrt 2))) (sqrt (sqrt 2)))

prune2.9s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.8b

regimes375.0ms

Accuracy

88% (2.8b remaining)

Error of 12.3b against oracle of 9.5b and baseline of 32.9b

bsearch346.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.6s1028×body2560valid
1.0s5986×body80valid
671.0ms881×body1280valid
390.0ms2978×body80nan
226.0ms439×body640valid
120.0ms212×body320valid
111.0ms117×body5120valid
60.0ms119×body160valid