Details

Time bar (total: 24.8s)

sample361.0ms

Algorithm
intervals
Results
92.0ms556×pre80true
86.0ms300×body80nan
53.0ms108×body320valid
32.0ms99×body160valid
11.0ms17×body640valid
5.0ms32×body80valid

simplify127.0ms

Calls
1 calls:
Slowest
126.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 51.4b

localize377.0ms

Local error

Found 4 expressions with local error:

27.3b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.1b
(fma c (* -4 a) (* b b))
0.1b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.0b
(sqrt (fma c (* -4 a) (* b b)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×fma-neg sqrt-prod
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×div-sub div-inv
1×rem-sqrt-square clear-num sub-neg frac-2neg flip3-- pow1/2 fma-udef flip-- associate-/l/
Calls
4 calls:
Slowest
16.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
12.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
1.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series380.0ms

Calls
4 calls:
Slowest
115.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
95.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
95.0ms
(sqrt (fma c (* -4 a) (* b b)))
74.0ms
(fma c (* -4 a) (* b b))

simplify618.0ms

Calls
26 calls:
Slowest
67.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
63.0ms
(- (pow b 2) (* 4 (* a c)))
55.0ms
(- (pow b 2) (* 4 (* a c)))
49.0ms
(- (pow b 2) (* 4 (* a c)))
45.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))

prune874.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 48.1b

localize15.0ms

Local error

Found 4 expressions with local error:

50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.1b
(fma c (* -4 a) (* b b))
0.1b
(fma c (* -4 a) (* b b))
0.1b
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×fma-udef
2×div-inv
1×clear-num frac-2neg associate-/l/
Calls
4 calls:
Slowest
6.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma c (* -4 a) (* b b))
0.0ms
(fma c (* -4 a) (* b b))

series1.1s

Calls
4 calls:
Slowest
574.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
402.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
75.0ms
(fma c (* -4 a) (* b b))
70.0ms
(fma c (* -4 a) (* b b))

simplify1.8s

Calls
16 calls:
Slowest
359.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
318.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
202.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
202.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
103.0ms
(* (cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)) (cbrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2)))

prune1.0s

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 48.0b

localize28.0ms

Local error

Found 4 expressions with local error:

50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.4b
(cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod fma-udef
1×pow1/3
Calls
4 calls:
Slowest
1.0ms
(cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.7s

Calls
4 calls:
Slowest
530.0ms
(cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))
416.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
410.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
366.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify2.6s

Calls
15 calls:
Slowest
373.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
373.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
366.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
287.0ms
(- (exp (* 1/3 (- (log -1) (log (/ 1 b))))) (+ (* 1/3 (/ (* (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) (exp (* 1/3 (- (log -1) (log (/ 1 b)))))) b)) (* 5/216 (* (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (* a c)) (pow (/ 1 (pow b 2)) 1/3)))))
267.0ms
(- (pow (/ -1 b) -1/3) (+ (* 5/216 (* (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6) (* a c)) (pow (/ 1 (pow b 2)) 1/3))) (* 1/3 (* (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) (pow (/ -1 (pow b 2)) 1/3)))))

prune912.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 47.6b

localize33.0ms

Local error

Found 4 expressions with local error:

50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
50.8b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.5b
(cbrt (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×cbrt-prod expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef
1×cbrt-div pow1/3 div-inv
Calls
4 calls:
Slowest
2.0ms
(cbrt (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

series1.8s

Calls
4 calls:
Slowest
589.0ms
(cbrt (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a))
446.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
419.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
389.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify3.5s

Calls
17 calls:
Slowest
481.0ms
(- (+ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (cbrt -1/2)) (* 5/216 (/ (* (exp (* 1/3 (+ (* 4 (log (/ -1 a))) (* 2 (log (/ -1 b)))))) (* (cbrt -1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 6))) c))) (* 1/3 (/ (* (exp (* 1/3 (- (log (/ -1 a)) (log (/ -1 b))))) (* (cbrt -1/2) (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2))) b)))
423.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
381.0ms
(- (* (cbrt 1/2) (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b)))))) (+ (* 5/216 (/ (* (cbrt 1/2) (* (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 6) (exp (* 1/3 (+ (* 2 (log (/ 1 b))) (* 4 (log (/ 1 a)))))))) c)) (* 1/3 (/ (* (cbrt 1/2) (* (exp (* 1/3 (- (+ (log (/ 1 a)) (log -1)) (log (/ 1 b))))) (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2))) b))))
363.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
357.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune697.0ms

Pruning

27 alts after pruning (26 fresh and 1 done)

Merged error: 47.6b

regimes683.0ms

Accuracy

0% (3.0b remaining)

Error of 51.8b against oracle of 48.8b and baseline of 51.8b

bsearch4.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
1.5s3651×body320valid
1.2s8317×body80nan
1.2s537×body640valid
906.0ms16317×pre80true
774.0ms2919×body160valid
140.0ms893×body80valid