Details

Time bar (total: 25.7s)

sample31.0ms

Algorithm
intervals
Results
21.0ms270×body80valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.8b

localize32.0ms

Local error

Found 2 expressions with local error:

22.8b
(/ (fma a c (* b d)) (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite10.0ms

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
3×associate-/r* associate-/l*
2×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-undiv clear-num frac-2neg div-exp fma-udef div-inv
Counts
2 → 41
Calls
2 calls:
Slowest
9.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series207.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
155.0ms
(/ (fma a c (* b d)) (fma d d (* c c)))
51.0ms
(fma a c (* b d))

simplify2.2s

Counts
57 → 47
Calls
57 calls:
Slowest
416.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (fma d d (* c c)) (fma d d (* c c))) (fma d d (* c c))))
169.0ms
(* (* (/ (fma a c (* b d)) (fma d d (* c c))) (/ (fma a c (* b d)) (fma d d (* c c)))) (/ (fma a c (* b d)) (fma d d (* c c))))
164.0ms
(* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d)))
80.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))
53.0ms
(/ (sqrt (fma a c (* b d))) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c)))))

prune678.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.4b

localize21.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma d d (* c c)))
24.7b
(sqrt (fma d d (* c c)))
16.0b
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
0.3b
(fma a c (* b d))

rewrite9.0ms

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
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×fma-udef associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
Slowest
5.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms
(sqrt (fma d d (* c c)))
1.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
144.0ms
(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
51.0ms
(sqrt (fma d d (* c c)))
50.0ms
(fma a c (* b d))
46.0ms
(sqrt (fma d d (* c c)))

simplify3.5s

Counts
118 → 99
Calls
118 calls:
Slowest
303.0ms
(/ (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))))
185.0ms
(* (* (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c))))) (/ (fma a c (* b d)) (sqrt (fma d d (* c c)))))
171.0ms
(* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d)))
73.0ms
(* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
65.0ms
(/ (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))) (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))))

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 18.7b

localize18.0ms

Local error

Found 3 expressions with local error:

22.5b
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
0.5b
(/ 1 (fma d d (* c c)))
0.3b
(fma a c (* b d))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×*-un-lft-identity times-frac
19×add-cube-cbrt
16×add-exp-log
13×associate-*r*
10×add-cbrt-cube
6×pow1
4×div-exp prod-exp
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative fma-udef pow-flip inv-pow
Counts
3 → 84
Calls
3 calls:
Slowest
10.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
4.0ms
(/ 1 (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series230.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
114.0ms
(* (fma a c (* b d)) (/ 1 (fma d d (* c c))))
65.0ms
(fma a c (* b d))
50.0ms
(/ 1 (fma d d (* c c)))

simplify7.9s

Counts
103 → 93
Calls
103 calls:
Slowest
803.0ms
(* (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))) (* (* (/ 1 (fma d d (* c c))) (/ 1 (fma d d (* c c)))) (/ 1 (fma d d (* c c)))))
385.0ms
(* (fma a c (* b d)) (/ (sqrt 1) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
339.0ms
(* (fma a c (* b d)) (/ (* (cbrt 1) (cbrt 1)) (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))
243.0ms
(exp (* (fma a c (* b d)) (/ 1 (fma d d (* c c)))))
229.0ms
(* (fma a c (* b d)) (/ 1 (* (cbrt (fma d d (* c c))) (cbrt (fma d d (* c c))))))

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 18.7b

localize58.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma d d (* c c)))
24.7b
(sqrt (fma d d (* c c)))
16.1b
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
0.3b
(fma a c (* b d))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
21×*-un-lft-identity add-cube-cbrt
18×times-frac sqrt-prod
6×pow1 add-cbrt-cube add-exp-log associate-/l*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* fma-udef
2×rem-sqrt-square sqrt-pow1 pow1/2 hypot-def
1×cbrt-undiv clear-num frac-2neg div-exp div-inv
Counts
4 → 87
Calls
4 calls:
Slowest
10.0ms
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
2.0ms
(sqrt (fma d d (* c c)))
2.0ms
(sqrt (fma d d (* c c)))
0.0ms
(fma a c (* b d))

series274.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
115.0ms
(/ (sqrt (fma d d (* c c))) (fma a c (* b d)))
61.0ms
(sqrt (fma d d (* c c)))
56.0ms
(sqrt (fma d d (* c c)))
42.0ms
(fma a c (* b d))

simplify3.8s

Counts
118 → 99
Calls
118 calls:
Slowest
466.0ms
(* (* (/ (sqrt (fma d d (* c c))) (fma a c (* b d))) (/ (sqrt (fma d d (* c c))) (fma a c (* b d)))) (/ (sqrt (fma d d (* c c))) (fma a c (* b d))))
267.0ms
(/ (* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c)))) (* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d))))
164.0ms
(* (* (fma a c (* b d)) (fma a c (* b d))) (fma a c (* b d)))
112.0ms
(* (* (sqrt (fma d d (* c c))) (sqrt (fma d d (* c c)))) (sqrt (fma d d (* c c))))
79.0ms
(/ (* (cbrt (sqrt (fma d d (* c c)))) (cbrt (sqrt (fma d d (* c c))))) (* (cbrt (fma a c (* b d))) (cbrt (fma a c (* b d)))))

prune1.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 18.7b

regimes381.0ms

Accuracy

0% (2.9b remaining)

Error of 25.5b against oracle of 22.6b and baseline of 25.5b

bsearch3.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.7s8528×body80valid