Details

Time bar (total: 3.0m)

sample135.0ms

Algorithm
intervals
Results
42.0ms196×body80valid
25.0ms29×body2560valid
20.0ms27×body1280valid
13.0ms99×body80nan
8.0ms14×body640valid
3.0ms6×body320valid
2.0ms2×body5120valid
1.0ms2×body160valid

simplify186.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
186.0ms
(/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.0b

localize31.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* a c) -4 (* b b)))
0.9b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))
0.1b
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
169×add-sqr-sqrt
168×*-un-lft-identity
159×times-frac
116×add-cube-cbrt
60×prod-diff
46×sqrt-prod
34×distribute-rgt-neg-in
26×distribute-lft-out-- difference-of-squares
25×associate-/l*
21×distribute-lft-neg-in
10×fma-neg
9×add-cbrt-cube add-exp-log
8×add-log-exp
7×neg-mul-1
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv associate-/r* 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 → 240
Calls
4 calls:
Slowest
30.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
23.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
2.0ms
(sqrt (fma (* a c) -4 (* b b)))
0.0ms
(fma (* a c) -4 (* b b))

series414.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
119.0ms
(sqrt (fma (* a c) -4 (* b b)))
99.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)
74.0ms
(fma (* a c) -4 (* b b))

simplify37.1s

Counts
394 → 252
Calls
394 calls:
Slowest
881.0ms
(* (* (/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a) (/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a)) (/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) 2) a))
486.0ms
(/ (/ (* (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b))))) (cbrt (- (- b) (sqrt (fma (* a c) -4 (* b b)))))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
454.0ms
(/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) a)
346.0ms
(+ (* (- b) (- b)) (+ (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* (- b) (sqrt (fma (* a c) -4 (* b b))))))
334.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))

prune3.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize44.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma a (* c -4) (* b b)))
11.4b
(/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b))
3.4b
(/ (/ (/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b)) 2) a)
0.4b
(- (sqrt (fma a (* c -4) (* b b))) b)

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
342×times-frac
199×add-sqr-sqrt
168×*-un-lft-identity
138×add-cube-cbrt
41×associate-/l*
33×add-cbrt-cube add-exp-log
30×sqrt-prod difference-of-squares
26×associate-/r/
18×prod-diff div-inv
15×cbrt-undiv div-exp distribute-lft-out--
14×flip3-- flip--
9×associate-/r*
6×fma-neg prod-exp cbrt-unprod add-log-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u
2×clear-num frac-2neg
1×rem-sqrt-square sub-neg sqrt-pow1 pow1/2 diff-log associate-/l/
Counts
4 → 279
Calls
4 calls:
Slowest
43.0ms
(/ (/ (/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b)) 2) a)
36.0ms
(/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b))
8.0ms
(- (sqrt (fma a (* c -4) (* b b))) b)
1.0ms
(sqrt (fma a (* c -4) (* b b)))

series754.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
274.0ms
(/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b))
251.0ms
(/ (/ (/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b)) 2) a)
131.0ms
(- (sqrt (fma a (* c -4) (* b b))) b)
98.0ms
(sqrt (fma a (* c -4) (* b b)))

simplify1.4m

Counts
442 → 291
Calls
442 calls:
Slowest
1.6s
(/ (/ (/ (* (* (* (* a a) a) (* (* 4 4) 4)) (* (* c c) c)) (* (* (- (sqrt (fma a (* c -4) (* b b))) b) (- (sqrt (fma a (* c -4) (* b b))) b)) (- (sqrt (fma a (* c -4) (* b b))) b))) (* (* 2 2) 2)) (* (* a a) a))
1.3s
(/ (/ (/ (* (* (* (* a 4) (* a 4)) (* a 4)) (* (* c c) c)) (* (* (- (sqrt (fma a (* c -4) (* b b))) b) (- (sqrt (fma a (* c -4) (* b b))) b)) (- (sqrt (fma a (* c -4) (* b b))) b))) (* (* 2 2) 2)) (* (* a a) a))
1.2s
(/ (/ (/ (* (* (* (* a 4) c) (* (* a 4) c)) (* (* a 4) c)) (* (* (- (sqrt (fma a (* c -4) (* b b))) b) (- (sqrt (fma a (* c -4) (* b b))) b)) (- (sqrt (fma a (* c -4) (* b b))) b))) (* (* 2 2) 2)) (* (* a a) a))
733.0ms
(/ (/ (/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b)) (cbrt 2)) (sqrt a))
638.0ms
(/ (/ (* (cbrt (/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b))) (cbrt (/ (* (* a 4) c) (- (sqrt (fma a (* c -4) (* b b))) b)))) (sqrt 2)) 1)

prune4.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.7b

localize27.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* c a) -4 (* b b)))
0.6b
(fma (* c a) -4 (* b b))
0.4b
(- (sqrt (fma (* c a) -4 (* b b))) b)
0.1b
(/ c (/ (- (sqrt (fma (* c a) -4 (* b b))) b) 2))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
135×add-sqr-sqrt
108×*-un-lft-identity
82×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/r*
18×prod-diff
13×distribute-lft-out--
9×add-cbrt-cube add-exp-log
6×fma-neg add-log-exp
5×pow1 div-inv
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×cbrt-undiv div-exp associate-/l*
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log associate-/r/ fma-udef flip--
Counts
4 → 178
Calls
4 calls:
Slowest
14.0ms
(/ c (/ (- (sqrt (fma (* c a) -4 (* b b))) b) 2))
8.0ms
(- (sqrt (fma (* c a) -4 (* b b))) b)
1.0ms
(sqrt (fma (* c a) -4 (* b b)))
0.0ms
(fma (* c a) -4 (* b b))

series607.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
263.0ms
(/ c (/ (- (sqrt (fma (* c a) -4 (* b b))) b) 2))
133.0ms
(- (sqrt (fma (* c a) -4 (* b b))) b)
125.0ms
(sqrt (fma (* c a) -4 (* b b)))
86.0ms
(fma (* c a) -4 (* b b))

simplify21.0s

Counts
280 → 190
Calls
280 calls:
Slowest
537.0ms
(- (* (sqrt (fma (* c a) -4 (* b b))) (sqrt (fma (* c a) -4 (* b b)))) (* b b))
441.0ms
(/ (* (cbrt c) (cbrt c)) (/ (* (cbrt (- (sqrt (fma (* c a) -4 (* b b))) b)) (cbrt (- (sqrt (fma (* c a) -4 (* b b))) b))) (* (cbrt 2) (cbrt 2))))
342.0ms
(* (* (- (sqrt (fma (* c a) -4 (* b b))) b) (- (sqrt (fma (* c a) -4 (* b b))) b)) (- (sqrt (fma (* c a) -4 (* b b))) b))
310.0ms
(- (pow (sqrt (fma (* c a) -4 (* b b))) 3) (pow b 3))
290.0ms
(/ (* (cbrt c) (cbrt c)) (/ 1 (* (cbrt 2) (cbrt 2))))

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.7b

localize40.0ms

Local error

Found 4 expressions with local error:

21.7b
(sqrt (fma (* a c) -4 (* b b)))
1.0b
(/ 1 (sqrt 2))
0.9b
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.6b
(fma (* a c) -4 (* b b))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
65×*-un-lft-identity
61×add-cube-cbrt
60×prod-diff
46×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
18×times-frac
10×fma-neg
8×add-exp-log add-log-exp
7×pow1 neg-mul-1
6×associate-/r* add-cbrt-cube
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×pow-flip associate-/l*
2×sqrt-pow1 pow1/2 diff-log div-exp distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 cbrt-undiv rem-sqrt-square rec-exp clear-num sub-neg frac-2neg flip3-- 1-exp neg-log fma-udef div-inv flip-- inv-pow
Counts
4 → 166
Calls
4 calls:
Slowest
27.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
5.0ms
(/ 1 (sqrt 2))
1.0ms
(sqrt (fma (* a c) -4 (* b b)))
1.0ms
(fma (* a c) -4 (* b b))

series311.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
120.0ms
(sqrt (fma (* a c) -4 (* b b)))
98.0ms
(fma (* a c) -4 (* b b))
92.0ms
(- (- b) (sqrt (fma (* a c) -4 (* b b))))
0.0ms
(/ 1 (sqrt 2))

simplify18.1s

Counts
259 → 176
Calls
259 calls:
Slowest
518.0ms
(- (pow (- b) 3) (pow (sqrt (fma (* a c) -4 (* b b))) 3))
346.0ms
(- (* (- b) (- b)) (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))))
271.0ms
(+ (* (- b) (- b)) (+ (* (sqrt (fma (* a c) -4 (* b b))) (sqrt (fma (* a c) -4 (* b b)))) (* (- b) (sqrt (fma (* a c) -4 (* b b))))))
262.0ms
(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))))))))
259.0ms
(* (/ 1 (sqrt 2)) (/ (/ (- (- b) (sqrt (fma (* a c) -4 (* b b)))) (sqrt 2)) a))

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.7b

regimes270.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.1b

bsearch357.0ms

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.2s1054×body2560valid
1.1s884×body1280valid
1.0s5901×body80valid
440.0ms2927×body80nan
235.0ms421×body640valid
147.0ms116×body5120valid
96.0ms229×body320valid
30.0ms118×body160valid