Details

Time bar (total: 3.8s)

sample20.0ms

Algorithm
intervals
Results
9.0ms278×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.2b
(+ (* a c) (* b d))
22.1b
(/ (+ (* 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)))

series143.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* c c) (* d d))
33.0ms
(+ (* a c) (* b d))
82.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify136.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune213.0ms

Filtered
70 candidates to 57 candidates (81.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 13.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.3b
(fma a c (* b d))
12.9b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
170×add-exp-log
92×prod-exp
63×div-exp
50×add-cbrt-cube
41×1-exp
17×cbrt-unprod
16×cbrt-undiv
15×rec-exp
14×add-sqr-sqrt
12×add-cube-cbrt *-un-lft-identity times-frac
9×pow1
7×associate-*r* associate-*l*
6×associate-/l*
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
2×pow-flip frac-2neg pow-prod-down clear-num associate-/r*
1×frac-times associate-*r/ associate-*l/ *-commutative fma-udef inv-pow unswap-sqr
Counts
4 → 145
Calls
4 calls:
4.0ms
(/ 1 (* (hypot c d) 1))
24.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms
(fma a c (* b d))
3.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series386.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (* (hypot c d) 1))
179.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
39.0ms
(fma a c (* b d))
115.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify46.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861191
11654892
25002884

prune286.0ms

Filtered
157 candidates to 77 candidates (49.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.3b
(fma a c (* b d))
12.9b
(/ (fma a c (* b d)) (hypot c d))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
40×times-frac
25×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
22×add-exp-log
17×add-cbrt-cube
16×associate-/l*
10×div-exp
7×cbrt-undiv
4×prod-exp associate-/r* div-inv
3×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
2×frac-2neg 1-exp clear-num cbrt-unprod
1×fma-udef associate-/l/
Counts
3 → 89
Calls
3 calls:
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))

series266.0ms

Counts
3 → 9
Calls
3 calls:
118.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
36.0ms
(fma a c (* b d))
112.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify76.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune266.0ms

Filtered
98 candidates to 76 candidates (77.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (hypot c d) (fma a c (* b d))))
0.2b
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
0.3b
(fma a c (* b d))
12.9b
(/ (hypot c d) (fma a c (* b d)))

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
249×add-exp-log
159×times-frac
120×div-exp
112×prod-exp
105×add-sqr-sqrt
93×*-un-lft-identity
91×add-cube-cbrt
64×1-exp
47×add-cbrt-cube
44×associate-*r*
43×rec-exp
19×cbrt-undiv
16×associate-/r*
12×pow1 cbrt-unprod
11×div-inv
7×associate-*l*
6×associate-/l*
5×pow-flip pow-prod-down unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×inv-pow
2×frac-2neg clear-num associate-/r/
1×frac-times associate-*r/ associate-*l/ un-div-inv *-commutative fma-udef
Counts
4 → 270
Calls
4 calls:
8.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
35.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
0.0ms
(fma a c (* b d))
2.0ms
(/ (hypot c d) (fma a c (* b d)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
117.0ms
(/ 1 (/ (hypot c d) (fma a c (* b d))))
182.0ms
(* (/ 1 (* (hypot c d) 1)) (/ 1 (/ (hypot c d) (fma a c (* b d)))))
37.0ms
(fma a c (* b d))
96.0ms
(/ (hypot c d) (fma a c (* b d)))

simplify95.0ms

Algorithm
egg-herbie
Counts
282 → 282
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
010202692
139782350
250022153

prune492.0ms

Filtered
282 candidates to 141 candidates (50.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.7b

regimes165.0ms

Accuracy

32.2% (7.8b remaining)

Error of 13.5b against oracle of 5.8b and baseline of 17.2b

bsearch80.0ms

Steps
ItersRangePoint
8
3.905534790569565e+76
3.5318877144286925e+79
3.47490452119893e+79
10
-8.119291710401494e+188
-2.6279527955229556e+170
-9.255264963641289e+170

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample496.0ms

Algorithm
intervals
Results
287.0ms8480×body80valid