Details

Time bar (total: 9.8s)

sample19.0ms

Algorithm
intervals
Results
9.0ms268×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(+ (* a c) (* b d))
24.6b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×add-log-exp
5×add-exp-log add-cbrt-cube
4×flip3-+ flip-+
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×+-commutative fma-def sum-log associate-/r/ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
3 → 61
Calls
3 calls:
3.0ms
(+ (* c c) (* d d))
2.0ms
(+ (* a c) (* b d))
11.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series148.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* c c) (* d d))
36.0ms
(+ (* a c) (* b d))
85.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify134.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune200.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 15.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.3b
(fma a c (* b d))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
15.0b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
155×add-exp-log
86×prod-exp
57×div-exp
45×add-cbrt-cube
35×1-exp
16×cbrt-unprod
14×cbrt-undiv
12×add-sqr-sqrt rec-exp
10×add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r* associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×div-inv associate-/l*
1×frac-times hypot-udef frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r* *-commutative fma-udef unswap-sqr
Counts
4 → 122
Calls
4 calls:
0.0ms
(hypot c d)
0.0ms
(fma a c (* b d))
21.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
3.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series376.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
37.0ms
(fma a c (* b d))
178.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
115.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify46.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
04861106
11625820
25001818

prune277.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.3b
(fma a c (* b d))
15.0b
(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
26×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
23×add-exp-log
18×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u prod-exp associate-/r* log1p-expm1-u div-inv add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×hypot-udef fma-udef associate-/l/
Counts
4 → 99
Calls
4 calls:
0.0ms
(hypot c d)
6.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms
(fma a c (* b d))
2.0ms
(/ (fma a c (* b d)) (hypot c d))

series313.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
114.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
40.0ms
(fma a c (* b d))
113.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify80.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0308794
11149701
23275701
35001693

prune319.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt (hypot c d)))
0.3b
(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
6.4b
(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
8.9b
(/ (fma a c (* b d)) (sqrt (hypot c d)))

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
5792×times-frac
2471×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1329×sqrt-prod
172×div-inv
105×associate-/r*
54×add-exp-log
36×div-exp
34×add-cbrt-cube
31×associate-/l*
25×associate-/r/
20×cbrt-undiv
6×pow1
4×expm1-log1p-u rec-exp frac-2neg 1-exp clear-num log1p-expm1-u add-log-exp
3×pow-flip
1×sqrt-pow1 pow1/2 associate-/l/ inv-pow
Counts
4 → 1883
Calls
4 calls:
3.0ms
(/ 1 (sqrt (hypot c d)))
55.0ms
(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
7.0ms
(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
3.0ms
(/ (fma a c (* b d)) (sqrt (hypot c d)))

series635.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ 1 (sqrt (hypot c d)))
184.0ms
(/ (/ 1 (sqrt (hypot c d))) (/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d)))))
162.0ms
(/ (hypot c d) (/ (fma a c (* b d)) (sqrt (hypot c d))))
205.0ms
(/ (fma a c (* b d)) (sqrt (hypot c d)))

simplify424.0ms

Algorithm
egg-herbie
Counts
1895 → 1895
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
0500149275

prune5.7s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.4b

regimes229.0ms

Accuracy

26% (8.7b remaining)

Error of 13.9b against oracle of 5.2b and baseline of 16.9b

bsearch67.0ms

Steps
ItersRangePoint
9
1.2335142670436914e+75
6.108550930002793e+80
6.020899153462114e+80
5
-6.754155808682356e+149
-1.7436095249739484e+149
-1.7747157524291317e+149

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04028
14228
24228

end0.0ms

sample484.0ms

Algorithm
intervals
Results
287.0ms8473×body80valid