Details

Time bar (total: 3.6s)

sample21.0ms

Algorithm
intervals
Results
9.0ms280×body80valid

simplify7.0ms

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: 27.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.5b
(+ (* a c) (* b d))
26.7b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite50.0ms

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:
8.0ms
(+ (* c c) (* d d))
10.0ms
(+ (* a c) (* b d))
31.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series146.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* c c) (* d d))
35.0ms
(+ (* a c) (* b d))
84.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify133.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune195.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 16.7b

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))
16.3b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite76.0ms

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:
11.0ms
(/ 1 (* (hypot c d) 1))
50.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms
(fma a c (* b d))
8.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series392.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 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))
120.0ms
(/ (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

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

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))
16.3b
(/ (fma a c (* b d)) (hypot c d))

rewrite21.0ms

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:
13.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
0.0ms
(fma a c (* b d))
5.0ms
(/ (fma a c (* b d)) (hypot c d))

series281.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
42.0ms
(fma a c (* b d))
118.0ms
(/ (fma a c (* b d)) (hypot c d))

simplify81.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0297767
11133677
23251677
35001670

prune252.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.2b
(* (* 1 (/ 1 (* (hypot c d) 1))) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.3b
(fma a c (* b d))
16.3b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite125.0ms

Algorithm
rewrite-expression-head
Rules
366×add-exp-log
262×prod-exp
120×div-exp
116×1-exp
68×add-cbrt-cube
30×cbrt-unprod
27×rec-exp
18×cbrt-undiv
12×pow1
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
7×associate-*r*
6×associate-/l*
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×associate-*r/ div-inv
2×frac-times pow-flip frac-2neg associate-*l/ clear-num associate-/r* un-div-inv
1×associate-*l* *-commutative fma-udef inv-pow
Counts
4 → 188
Calls
4 calls:
11.0ms
(/ 1 (* (hypot c d) 1))
95.0ms
(* (* 1 (/ 1 (* (hypot c d) 1))) (/ (fma a c (* b d)) (* (hypot c d) 1)))
0.0ms
(fma a c (* b d))
8.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

series394.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 1 (* (hypot c d) 1))
180.0ms
(* (* 1 (/ 1 (* (hypot c d) 1))) (/ (fma a c (* b d)) (* (hypot c d) 1)))
43.0ms
(fma a c (* b d))
119.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify53.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
07911674
118791235
250021224

prune225.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 5.2b

regimes177.0ms

Accuracy

33.6% (7.5b remaining)

Error of 13.4b against oracle of 5.9b and baseline of 17.1b

bsearch62.0ms

Steps
ItersRangePoint
6
1.4211719871959458e+151
1.5804785112129858e+152
4.355931456769411e+151
10
-9.74529748598903e+204
-2.833408922216708e+192
-3.9421165304259007e+195

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02714
13014
23014

end0.0ms

sample540.0ms

Algorithm
intervals
Results
267.0ms8450×body80valid