Details

Time bar (total: 24.5s)

sample169.0ms

Algorithm
intervals
Results
50.0ms272×body80nan
47.0ms174×body160valid
30.0ms528×pre80true
14.0ms36×body320valid
6.0ms46×body80valid

simplify175.0ms

Calls
1 calls:
Slowest
175.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.9b

localize26.0ms

Local error

Found 4 expressions with local error:

39.6b
(- (sqrt (fma c (* -4 a) (* b b))) b)
0.2b
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
0.1b
(fma c (* -4 a) (* b b))
0.0b
(sqrt (fma c (* -4 a) (* b b)))

rewrite25.0ms

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
14.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
7.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms
(sqrt (fma c (* -4 a) (* b b)))
0.0ms
(fma c (* -4 a) (* b b))

series414.0ms

Calls
4 calls:
Slowest
124.0ms
(/ (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2) a)
123.0ms
(- (sqrt (fma c (* -4 a) (* b b))) b)
96.0ms
(sqrt (fma c (* -4 a) (* b b)))
71.0ms
(fma c (* -4 a) (* b b))

simplify649.0ms

Calls
26 calls:
Slowest
66.0ms
(* (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)) (cbrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2)))
65.0ms
(sqrt (/ (- (sqrt (fma c (* -4 a) (* b b))) b) 2))
60.0ms
(- (pow b 2) (* 4 (* a c)))
60.0ms
(- (pow b 2) (* 4 (* a c)))
50.0ms
(- (pow b 2) (* 4 (* a c)))

prune907.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 41.4b

localize20.0ms

Local error

Found 4 expressions with local error:

44.1b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
0.2b
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
0.1b
(fma c (* -4 a) (* b b))
0.1b
(fma c (* -4 a) (* b b))

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))

series1.2s

Calls
4 calls:
Slowest
625.0ms
(/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a)
467.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
86.0ms
(fma c (* -4 a) (* b b))
67.0ms
(fma c (* -4 a) (* b b))

simplify1.8s

Calls
16 calls:
Slowest
324.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) a)) (* 1/2 (/ b a)))
319.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
266.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)
163.0ms
(- (* 1/2 (/ (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) a)) (* 1/2 (/ b a)))
109.0ms
(sqrt (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2))

prune987.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 41.4b

localize26.0ms

Local error

Found 4 expressions with local error:

44.1b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
44.1b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
44.1b
(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))

rewrite5.0ms

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
3.0ms
(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
555.0ms
(cbrt (/ (/ (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)) 2) a))
418.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
407.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
381.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify3.3s

Calls
17 calls:
Slowest
487.0ms
(- (+ (* (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)))
436.0ms
(- (* (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))))
375.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
340.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
318.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)

prune996.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 40.9b

localize19.0ms

Local error

Found 4 expressions with local error:

44.1b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
44.1b
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
44.1b
(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)))

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))

series1.9s

Calls
4 calls:
Slowest
593.0ms
(cbrt (fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b)))
457.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
448.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))
428.0ms
(fma (sqrt (sqrt (fma c (* -4 a) (* b b)))) (sqrt (sqrt (fma c (* -4 a) (* b b)))) (- b))

simplify2.6s

Calls
15 calls:
Slowest
421.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
377.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
353.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c)))))) 2) b)
302.0ms
(- (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)))))
272.0ms
(- (pow (exp (* 1/4 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a)))))) 2) b)

prune824.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 40.9b

regimes656.0ms

Accuracy

0% (3.3b remaining)

Error of 43.2b against oracle of 39.9b and baseline of 43.2b

bsearch5.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
1.7s8651×body80nan
1.5s4905×body160valid
1.1s16651×pre80true
1.0s1333×body320valid
278.0ms1762×body80valid