Details

Time bar (total: 44.3s)

sample97.0ms

Algorithm
intervals
Results
57.0ms278×body80valid
20.0ms100×body80nan

simplify229.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
229.0ms
(if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a)))

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.2b

localize154.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))
0.9b
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
0.6b
(fma -4 (* c a) (* b b))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
60×prod-diff
53×add-sqr-sqrt
51×*-un-lft-identity
47×add-cube-cbrt
37×sqrt-prod
22×distribute-rgt-neg-in
21×distribute-lft-neg-in
10×fma-neg
8×add-log-exp
7×neg-mul-1
6×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×rem-sqrt-square sqrt-pow1 pow1/2 diff-log distribute-lft-out-- difference-of-squares
1×associate--l- neg-sub0 sub-neg flip3-- neg-log fma-udef flip--
Counts
4 → 134
Calls
4 calls:
Slowest
10.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
3.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
0.0ms
(fma -4 (* c a) (* b b))

series451.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(sqrt (fma -4 (* c a) (* b b)))
131.0ms
(sqrt (fma -4 (* c a) (* b b)))
109.0ms
(- (- b) (sqrt (fma -4 (* c a) (* b b))))
77.0ms
(fma -4 (* c a) (* b b))

simplify16.4s

Counts
212 → 146
Calls
212 calls:
Slowest
309.0ms
(+ (* (- b) (- b)) (+ (* (sqrt (fma -4 (* c a) (* b b))) (sqrt (fma -4 (* c a) (* b b)))) (* (- b) (sqrt (fma -4 (* c a) (* b b))))))
299.0ms
(- (* (- b) (- b)) (* (sqrt (fma -4 (* c a) (* b b))) (sqrt (fma -4 (* c a) (* b b)))))
252.0ms
(fma (* (cbrt (- b)) (cbrt (- b))) (cbrt (- b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
251.0ms
(fma (sqrt b) (- (sqrt b)) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))
243.0ms
(fma 1 (- b) (- (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (* (cbrt (sqrt (fma -4 (* c a) (* b b)))) (cbrt (sqrt (fma -4 (* c a) (* b b))))))))

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.0b

localize150.0ms

Local error

Found 4 expressions with local error:

21.9b
(sqrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))
8.8b
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
9×sqrt-prod
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×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 prod-diff
1×sub-neg flip3-- fma-neg diff-log flip-- difference-of-squares
Counts
4 → 68
Calls
4 calls:
Slowest
20.0ms
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
116.0ms
(- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)
113.0ms
(sqrt (fma -4 (* c a) (* b b)))
107.0ms
(sqrt (fma -4 (* c a) (* b b)))
100.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify4.2s

Counts
89 → 80
Calls
89 calls:
Slowest
467.0ms
(- (* (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))) (* b b))
432.0ms
(* (* (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)) (- (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b))
244.0ms
(/ (exp (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))) (exp b))
232.0ms
(+ (* (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b)))))) (+ (* b b) (* (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) b)))
189.0ms
(- (pow (* (sqrt (sqrt (fma -4 (* c a) (* b b)))) (sqrt (sqrt (fma -4 (* c a) (* b b))))) 3) (pow b 3))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize237.0ms

Local error

Found 4 expressions with local error:

22.6b
(cbrt (fma -4 (* c a) (* b b)))
22.6b
(cbrt (fma -4 (* c a) (* b b)))
22.6b
(cbrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
2.0ms
(sqrt (fma -4 (* c a) (* b b)))
2.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))

series878.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
265.0ms
(cbrt (fma -4 (* c a) (* b b)))
259.0ms
(cbrt (fma -4 (* c a) (* b b)))
247.0ms
(cbrt (fma -4 (* c a) (* b b)))
107.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify4.9s

Counts
77 → 70
Calls
77 calls:
Slowest
352.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
347.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
341.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
329.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
293.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.0b

localize197.0ms

Local error

Found 4 expressions with local error:

22.6b
(cbrt (fma -4 (* c a) (* b b)))
22.6b
(cbrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))
21.9b
(sqrt (fma -4 (* c a) (* b b)))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×cbrt-prod pow1 sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 60
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(sqrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))
1.0ms
(cbrt (fma -4 (* c a) (* b b)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
626.0ms
(cbrt (fma -4 (* c a) (* b b)))
287.0ms
(cbrt (fma -4 (* c a) (* b b)))
133.0ms
(sqrt (fma -4 (* c a) (* b b)))
95.0ms
(sqrt (fma -4 (* c a) (* b b)))

simplify4.2s

Counts
78 → 72
Calls
78 calls:
Slowest
399.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
353.0ms
(- (pow b 2/3) (* 4/3 (* (* a c) (pow (/ 1 (pow b 4)) 1/3))))
325.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
301.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ 1 a)) (log (/ 1 c))))))
223.0ms
(exp (* 1/3 (- (log -4) (+ (log (/ -1 c)) (log (/ -1 a))))))

prune1.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.0b

regimes304.0ms

Accuracy

91.3% (0.6b remaining)

Error of 12.8b against oracle of 12.2b and baseline of 19.2b

bsearch123.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.0s8715×body80valid
605.0ms2926×body80nan