Details

Time bar (total: 27.2s)

sample61.0ms

Algorithm
intervals
Results
43.0ms266×body80valid

simplify110.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
110.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize18.0ms

Local error

Found 2 expressions with local error:

22.9b
(/ (- (* b c) (* a d)) (fma d d (* c c)))
0.3b
(- (* b c) (* a d))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×times-frac
4×add-cbrt-cube add-exp-log add-log-exp
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 flip3-- insert-posit16 log1p-expm1-u flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
2 → 50
Calls
2 calls:
Slowest
21.0ms
(- (* b c) (* a d))
18.0ms
(/ (- (* b c) (* a d)) (fma d d (* c c)))

series188.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
132.0ms
(/ (- (* b c) (* a d)) (fma d d (* c c)))
56.0ms
(- (* b c) (* a d))

simplify2.2s

Counts
37 → 56
Calls
37 calls:
Slowest
540.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
298.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
219.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
139.0ms
(/ (exp (* b c)) (exp (* a d)))
94.0ms
(/ (- (* b c) (* a d)) (fma d d (* c c)))

prune490.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.5b

localize43.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (fma d d (* c c)))
25.9b
(sqrt (fma d d (* c c)))
12.5b
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.3b
(- (* b c) (* a d))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 fma-udef hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
33.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
16.0ms
(- (* b c) (* a d))
3.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
131.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
57.0ms
(sqrt (fma d d (* c c)))
48.0ms
(sqrt (fma d d (* c c)))
47.0ms
(- (* b c) (* a d))

simplify3.0s

Counts
74 → 108
Calls
74 calls:
Slowest
369.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
332.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
196.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
132.0ms
(/ (exp (* b c)) (exp (* a d)))
102.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 19.4b

localize39.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (fma d d (* c c)))
25.9b
(sqrt (fma d d (* c c)))
12.5b
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.3b
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
95×add-sqr-sqrt
76×times-frac
53×*-un-lft-identity
47×add-cube-cbrt sqrt-prod
28×add-exp-log
22×associate-*r* associate-*l*
18×add-cbrt-cube
15×unswap-sqr
9×div-exp
8×pow1 prod-exp
6×associate-/r*
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp fma-udef hypot-def associate-/l/
1×frac-times clear-num frac-2neg flip3-- div-sub pow-prod-down associate-*l/ associate-*r/ *-commutative flip--
Counts
4 → 165
Calls
4 calls:
Slowest
37.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
26.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))))
3.0ms
(sqrt (fma d d (* c c)))
3.0ms
(sqrt (fma d d (* c c)))

series415.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
158.0ms
(* (/ 1 (sqrt (fma d d (* c c)))) (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))))
146.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
58.0ms
(sqrt (fma d d (* c c)))
53.0ms
(sqrt (fma d d (* c c)))

simplify10.6s

Counts
160 → 177
Calls
160 calls:
Slowest
366.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
298.0ms
(* 1 (/ (- (* b c) (* a d)) (sqrt (fma d d (* c c)))))
296.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
280.0ms
(* (* (* (/ 1 (sqrt (fma d d (* c c)))) (/ 1 (sqrt (fma d d (* c c))))) (/ 1 (sqrt (fma d d (* c c))))) (/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))))
261.0ms
(* (/ (* (* 1 1) 1) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))) (/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))))

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.4b

localize47.0ms

Local error

Found 4 expressions with local error:

25.9b
(sqrt (fma d d (* c c)))
25.9b
(sqrt (fma d d (* c c)))
12.5b
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
0.3b
(- (* b c) (* a d))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 associate-/r* add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×associate-/l*
2×rem-sqrt-square sqrt-pow1 flip3-- pow1/2 fma-udef hypot-def flip-- associate-/l/
1×cbrt-undiv clear-num sub-neg frac-2neg fma-neg diff-log div-sub div-exp prod-diff div-inv
Counts
4 → 96
Calls
4 calls:
Slowest
16.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
8.0ms
(- (* b c) (* a d))
2.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))

series301.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
56.0ms
(sqrt (fma d d (* c c)))
56.0ms
(sqrt (fma d d (* c c)))
44.0ms
(- (* b c) (* a d))

simplify3.0s

Counts
74 → 108
Calls
74 calls:
Slowest
355.0ms
(/ (* (* (- (* b c) (* a d)) (- (* b c) (* a d))) (- (* b c) (* a d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
310.0ms
(- (pow (* b c) 3) (pow (* a d) 3))
203.0ms
(- (* (* b c) (* b c)) (* (* a d) (* a d)))
139.0ms
(/ (exp (* b c)) (exp (* a d)))
108.0ms
(/ (- (* b c) (* a d)) (sqrt (sqrt (fma d d (* c c)))))

prune1.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 15.4b

regimes323.0ms

Accuracy

0.9% (7.0b remaining)

Error of 25.5b against oracle of 18.5b and baseline of 25.6b

bsearch53.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.3s8475×body80valid