Details

Time bar (total: 4.4s)

sample27.0ms

Algorithm
intervals
Results
16.0ms270×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0177
1217
2217

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.9b
(+ (* a c) (* b d))
27.3b
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite20.0ms

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))
3.0ms
(+ (* a c) (* b d))
12.0ms
(/ (+ (* 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))
83.0ms
(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify139.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0290532
11199475
24872462
35001462

prune214.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.7b

localize15.0ms

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))
17.2b
(/ (fma a c (* b d)) (* (hypot c d) 1))

rewrite39.0ms

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:
5.0ms
(/ 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))

series384.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ 1 (* (hypot c d) 1))
180.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (fma a c (* b d)) (* (hypot c d) 1)))
39.0ms
(fma a c (* b d))
112.0ms
(/ (fma a c (* b d)) (* (hypot c d) 1))

simplify49.0ms

Algorithm
egg-herbie
Counts
157 → 157
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04861191
11654892
25002884

prune289.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.5b

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))
17.2b
(/ (fma a c (* b d)) (hypot c d))

rewrite12.0ms

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:
7.0ms
(/ (/ (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:
114.0ms
(/ (/ (fma a c (* b d)) (hypot c d)) (* (hypot c d) 1))
39.0ms
(fma a c (* b d))
114.0ms
(/ (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

prune286.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (hypot c d))
0.5b
(* (cbrt (hypot c d)) (cbrt (hypot c d)))
5.4b
(/ (fma a c (* b d)) (cbrt (hypot c d)))
12.0b
(* (/ 1 (* (cbrt (hypot c d)) (cbrt (hypot c d)))) (/ (fma a c (* b d)) (cbrt (hypot c d))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
53×add-exp-log
51×times-frac
46×*-un-lft-identity
43×cbrt-prod add-cube-cbrt
28×associate-*r*
21×prod-exp
19×add-cbrt-cube
16×div-exp
13×pow1 associate-*l* unswap-sqr
9×cbrt-unprod
8×cbrt-undiv
7×pow1/3
6×swap-sqr associate-/r*
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow-prod-down div-inv associate-/l*
2×pow-sqr *-commutative pow-prod-up
1×pow2 frac-times frac-2neg pow-plus associate-*r/ associate-*l/ clear-num
Counts
4 → 168
Calls
4 calls:
1.0ms
(cbrt (hypot c d))
6.0ms
(* (cbrt (hypot c d)) (cbrt (hypot c d)))
3.0ms
(/ (fma a c (* b d)) (cbrt (hypot c d)))
39.0ms
(* (/ 1 (* (cbrt (hypot c d)) (cbrt (hypot c d)))) (/ (fma a c (* b d)) (cbrt (hypot c d))))

series620.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(cbrt (hypot c d))
126.0ms
(* (cbrt (hypot c d)) (cbrt (hypot c d)))
268.0ms
(/ (fma a c (* b d)) (cbrt (hypot c d)))
116.0ms
(* (/ 1 (* (cbrt (hypot c d)) (cbrt (hypot c d)))) (/ (fma a c (* b d)) (cbrt (hypot c d))))

simplify88.0ms

Algorithm
egg-herbie
Counts
180 → 180
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
06361899
131261666
250011538

prune526.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.4b

regimes267.0ms

Accuracy

36.3% (6.9b remaining)

Error of 12.9b against oracle of 6.0b and baseline of 16.8b

bsearch55.0ms

Steps
ItersRangePoint
7
5.1578966356472864e+168
2.0698913095985625e+170
3.2040013395502375e+169
4
-1.4453345422823506e+110
-8.371467560022169e+109
-1.4263286739610966e+110

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02915
13315
23315

end0.0ms

sample749.0ms

Algorithm
intervals
Results
528.0ms8459×body80valid