Details

Time bar (total: 1.1m)

sample79.0ms

Algorithm
intervals
Results
18.0ms200×body80valid
16.0ms22×body2560valid
15.0ms34×body1280valid
9.0ms104×body80nan
4.0ms11×body640valid
1.0ms2×body5120valid
1.0ms5×body320valid
0.0ms1×body160valid

simplify155.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
155.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.0b

localize20.0ms

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)

rewrite36.0ms

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
16.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
14.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
3.0ms
(sqrt (fma c (* -4 a) (* b b)))

series322.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
135.0ms
(sqrt (fma c (* -4 a) (* b b)))
103.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
83.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)

simplify14.2s

Counts
222 → 177
Calls
222 calls:
Slowest
489.0ms
(/ (/ (* (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)))
235.0ms
(/ (* (* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (* (* a a) a))
222.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (sqrt 2)) (* (cbrt a) (cbrt a)))
206.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) (sqrt a))
176.0ms
(/ (/ (* (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b)) (cbrt (- (sqrt (fma c (* -4 a) (* b b))) b))) (* (cbrt 2) (cbrt 2))) 1)

prune2.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 26.6b

localize23.0ms

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))

rewrite41.0ms

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
30.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series320.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
136.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
100.0ms
(sqrt (fma c (* -4 a) (* b b)))
84.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)

simplify7.4s

Counts
123 → 136
Calls
123 calls:
Slowest
320.0ms
(* (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) (/ 1 a))
294.0ms
(+ (log (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (- 0 (log a)))
258.0ms
(* (/ (* (* (- (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)))
255.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (- 0 (log a)))
255.0ms
(+ (- (log (- (sqrt (fma c (* -4 a) (* b b))) b)) (log 2)) (log (/ 1 a)))

prune1.9s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 26.6b

localize53.0ms

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)

rewrite96.0ms

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
79.0ms
(* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a))
8.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series776.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
429.0ms
(* (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) 1) (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a))
124.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
113.0ms
(sqrt (fma c (* -4 a) (* b b)))
110.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify22.7s

Counts
296 → 297
Calls
296 calls:
Slowest
792.0ms
(* (/ (* (* (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)))
624.0ms
(* (* (* (/ (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)))
498.0ms
(* (/ (sqrt (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) 1) (sqrt (/ (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) a)))
287.0ms
(* (/ (* (* (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)))
266.0ms
(+ (- (log (sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))) 0) (- (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

localize64.0ms

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)

rewrite22.0ms

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
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)))
1.0ms
(sqrt (fma c (* -4 a) (* b b)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(sqrt (fma c (* -4 a) (* b b)))
114.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
105.0ms
(sqrt (fma c (* -4 a) (* b b)))
102.0ms
(sqrt (fma c (* -4 a) (* b b)))

simplify2.1s

Counts
74 → 102
Calls
74 calls:
Slowest
95.0ms
(/ (exp (sqrt (fma c (* -4 a) (* b b)))) (exp b))
90.0ms
(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)))
84.0ms
(fma (sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b))))) (sqrt (cbrt (fma c (* -4 a) (* b b)))) (- (* (cbrt b) (* (cbrt b) (cbrt b)))))
78.0ms
(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)))))
69.0ms
(fma (sqrt (* (cbrt (fma c (* -4 a) (* b b))) (cbrt (fma c (* -4 a) (* b b))))) (sqrt (cbrt (fma c (* -4 a) (* b b)))) (- (* b 1)))

prune1.9s

Pruning

16 alts after pruning (13 fresh and 3 done)

Merged error: 26.6b

regimes501.0ms

Accuracy

86.7% (0.6b remaining)

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

bsearch193.0ms

end0.0ms

sample5.0s

Algorithm
intervals
Results
1.4s5763×body80valid
1.1s1113×body2560valid
848.0ms2958×body80nan
700.0ms883×body1280valid
317.0ms486×body640valid
194.0ms115×body5120valid
87.0ms224×body320valid
35.0ms122×body160valid