Details

Time bar (total: 1.1m)

sample103.0ms

Algorithm
intervals
Results
31.0ms200×body80valid
21.0ms34×body1280valid
13.0ms22×body2560valid
11.0ms104×body80nan
5.0ms11×body640valid
2.0ms5×body320valid
2.0ms2×body5120valid
0.0ms1×body160valid

simplify149.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
149.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize22.0ms

Local error

Found 3 expressions with local error:

20.6b
(sqrt (fma c (* -4 a) (* b b)))
0.2b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
138×times-frac
134×add-sqr-sqrt
107×*-un-lft-identity
81×add-cube-cbrt
28×sqrt-prod
26×difference-of-squares
22×associate-/l*
18×prod-diff
13×distribute-lft-out--
8×add-cbrt-cube add-exp-log
6×fma-neg
5×div-inv add-log-exp
4×pow1
3×expm1-log1p-u cbrt-undiv associate-/r* div-exp insert-posit16 log1p-expm1-u
2×div-sub
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 flip3-- pow1/2 diff-log flip-- associate-/l/
Counts
3 → 168
Calls
3 calls:
Slowest
33.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
15.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series328.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
123.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
108.0ms
(sqrt (fma c (* -4 a) (* b b)))
98.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify14.2s

Counts
222 → 177
Calls
222 calls:
Slowest
450.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (* (cbrt a) (cbrt a)))
409.0ms
(fma (sqrt 1) (sqrt (fma c (* -4 a) (* b b))) (- (* (sqrt b) (sqrt b))))
226.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
201.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
163.0ms
(/ (/ (- (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt b)) (cbrt 2)) (cbrt a))

prune2.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 26.6b

localize22.0ms

Local error

Found 3 expressions with local error:

20.6b
(sqrt (fma c (* -4 a) (* b b)))
0.2b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
45×*-un-lft-identity
35×add-cube-cbrt
34×times-frac
25×add-exp-log
22×associate-*l*
19×sqrt-prod
18×prod-diff
15×add-cbrt-cube
13×associate-*r*
8×div-exp prod-exp difference-of-squares
6×pow1 fma-neg unswap-sqr
5×add-log-exp
4×cbrt-undiv cbrt-unprod distribute-lft-out--
3×expm1-log1p-u insert-posit16 log1p-expm1-u
2×rec-exp 1-exp div-inv
1×frac-times rem-sqrt-square sub-neg sqrt-pow1 flip3-- pow1/2 diff-log pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative flip--
Counts
3 → 127
Calls
3 calls:
Slowest
36.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
13.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series333.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
120.0ms
(sqrt (fma c (* -4 a) (* b b)))
116.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
97.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify7.2s

Counts
123 → 136
Calls
123 calls:
Slowest
282.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
270.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- (log 1) (log a)))
267.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (log (/ 1 a)))
262.0ms
(* (/ (* (* (- (sqrt (fma c (* -4 a) (* b b))) b) (- (sqrt (fma c (* -4 a) (* b b))) b)) (- (sqrt (fma c (* -4 a) (* b b))) b)) (* (* 2 2) 2)) (/ (* (* 1 1) 1) (* (* a a) a)))
242.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))

prune1.8s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 26.6b

localize47.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma c (* -4 a) (* b b)))
20.6b
(sqrt (fma c (* -4 a) (* b b)))
0.3b
(* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a))
0.2b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
320×add-sqr-sqrt
318×times-frac
199×sqrt-prod
188×*-un-lft-identity
138×add-cube-cbrt
79×associate-*r* associate-*l*
38×difference-of-squares
28×unswap-sqr
21×add-exp-log
19×distribute-lft-out--
18×prod-diff
16×add-cbrt-cube
8×pow1 div-inv
7×div-exp
6×fma-neg prod-exp add-log-exp
4×expm1-log1p-u cbrt-undiv cbrt-unprod insert-posit16 log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 1-exp
1×frac-times sub-neg flip3-- diff-log pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 285
Calls
4 calls:
Slowest
104.0ms
(* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a))
15.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
2.0ms
(sqrt (fma c (* -4 a) (* b b)))

series755.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
397.0ms
(* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a))
127.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
119.0ms
(sqrt (fma c (* -4 a) (* b b)))
112.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify22.2s

Counts
296 → 297
Calls
296 calls:
Slowest
765.0ms
(* (/ (* (* (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (* (* 1 1) 1)) (* (* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a)) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a)))
616.0ms
(* (* (* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1)) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1)) (* (* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a)) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a)))
398.0ms
(/ (sqrt (/ (sqrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (sqrt 2))) (* (cbrt 1) (cbrt 1)))
297.0ms
(* (/ (* (* (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (* (* 1 1) 1)) (/ (* (* (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (* (* a a) a)))
252.0ms
(+ (- (log (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (log 1)) (- (log (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) (log a)))

prune5.0s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 26.6b

localize60.0ms

Local error

Found 4 expressions with local error:

20.6b
(sqrt (fma c (* -4 a) (* b b)))
20.6b
(sqrt (fma c (* -4 a) (* b b)))
20.6b
(sqrt (fma c (* -4 a) (* b b)))
0.2b
(- (sqrt (fma c (* -4 a) (* b b))) b)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
23×*-un-lft-identity
22×sqrt-prod
21×add-cube-cbrt
18×prod-diff
7×pow1
6×fma-neg add-log-exp
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
3×rem-sqrt-square sqrt-pow1 pow1/2
2×difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 90
Calls
4 calls:
Slowest
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
12.0ms
(sqrt (fma c (* -4 a) (* b b)))
3.0ms
(sqrt (fma c (* -4 a) (* b b)))
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series458.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
132.0ms
(sqrt (fma c (* -4 a) (* b b)))
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
107.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
106.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify2.0s

Counts
74 → 102
Calls
74 calls:
Slowest
119.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
75.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* b 1)))
75.0ms
(fma (* (cbrt (sqrt (fma c (* -4 a) (* b b)))) (cbrt (sqrt (fma c (* -4 a) (* b b))))) (cbrt (sqrt (fma c (* -4 a) (* b b)))) (- (* (sqrt b) (sqrt b))))
66.0ms
(/ (exp (sqrt (fma c (* -4 a) (* b b)))) (exp b))
63.0ms
(fma 1 (sqrt (fma c (* -4 a) (* b b))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))

prune1.8s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 26.6b

regimes471.0ms

Accuracy

86.7% (0.6b remaining)

Error of 29.9b against oracle of 29.3b and baseline of 34.1b

bsearch175.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.3s1113×body2560valid
922.0ms5763×body80valid
857.0ms2958×body80nan
760.0ms883×body1280valid
331.0ms486×body640valid
143.0ms115×body5120valid
129.0ms224×body320valid
35.0ms122×body160valid