Details

Time bar (total: 3.8s)

sample20.0ms

Algorithm
intervals
Results
9.0ms269×body80valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0217
1407
2567
3767
4907
5947
6947

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* c c) (* d d))
0.4b
(- (* b c) (* a d))
24.7b
(/ (- (* b c) (* a 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
3×pow1 expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg fma-def frac-2neg fma-neg diff-log div-sub div-exp prod-diff clear-num sum-log div-inv
Counts
3 → 64
Calls
3 calls:
3.0ms
(+ (* c c) (* d d))
3.0ms
(- (* b c) (* a d))
10.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

series150.0ms

Counts
3 → 9
Calls
3 calls:
26.0ms
(+ (* c c) (* d d))
40.0ms
(- (* b c) (* a d))
84.0ms
(/ (- (* b c) (* a d)) (+ (* c c) (* d d)))

simplify42.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0314555
11341496
25001481

prune192.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (* (hypot c d) 1))
0.3b
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
0.4b
(- (* b c) (* a d))
15.2b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
83×add-exp-log
38×prod-exp
32×add-cbrt-cube
29×div-exp
28×add-sqr-sqrt
25×times-frac
23×add-cube-cbrt *-un-lft-identity
18×1-exp
13×associate-*r*
10×cbrt-undiv
9×pow1 rec-exp cbrt-unprod
7×associate-*l*
6×associate-/l* add-log-exp
4×expm1-log1p-u associate-/r* log1p-expm1-u div-inv
2×flip3-- pow-flip frac-2neg pow-prod-down clear-num flip-- associate-/l/ unswap-sqr
1×frac-times sub-neg fma-neg diff-log div-sub associate-*r/ prod-diff associate-*l/ *-commutative inv-pow
Counts
4 → 143
Calls
4 calls:
4.0ms
(/ 1 (* (hypot c d) 1))
24.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series377.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(/ 1 (* (hypot c d) 1))
171.0ms
(* (/ 1 (* (hypot c d) 1)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
113.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify64.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05531207
123041003
25001995

prune320.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot c d)
0.1b
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
0.4b
(- (* b c) (* a d))
15.2b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
54×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×associate-/l*
11×add-exp-log add-cbrt-cube
6×associate-/r* div-inv add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×div-sub associate-/l/
2×flip3-- frac-2neg clear-num flip--
1×sub-neg hypot-udef fma-neg diff-log prod-diff
Counts
4 → 131
Calls
4 calls:
0.0ms
(hypot c d)
9.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series313.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(hypot c d)
115.0ms
(/ (/ (- (* b c) (* a d)) (hypot c d)) (hypot c d))
38.0ms
(- (* b c) (* a d))
114.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify52.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04581435
116671331
250011322

prune367.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (hypot c d))
0.3b
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
0.4b
(- (* b c) (* a d))
15.2b
(/ (- (* b c) (* a d)) (hypot c d))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
43×times-frac
36×*-un-lft-identity
34×add-cube-cbrt
32×add-exp-log
20×add-cbrt-cube
13×associate-*r* associate-*l*
11×div-exp
8×prod-exp
7×pow1
6×cbrt-undiv associate-/r* associate-/l* add-log-exp unswap-sqr
4×expm1-log1p-u cbrt-unprod log1p-expm1-u div-inv
3×rec-exp 1-exp
2×flip3-- frac-2neg clear-num flip-- associate-/l/
1×frac-times sub-neg pow-flip fma-neg diff-log div-sub associate-*r/ prod-diff pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 139
Calls
4 calls:
2.0ms
(/ 1 (hypot c d))
18.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
3.0ms
(- (* b c) (* a d))
7.0ms
(/ (- (* b c) (* a d)) (hypot c d))

series392.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(/ 1 (hypot c d))
178.0ms
(* (/ 1 (hypot c d)) (/ (- (* b c) (* a d)) (hypot c d)))
38.0ms
(- (* b c) (* a d))
119.0ms
(/ (- (* b c) (* a d)) (hypot c d))

simplify65.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04901189
122601039
250011009

prune336.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.8b

regimes239.0ms

Accuracy

31.5% (8.6b remaining)

Error of 13.2b against oracle of 4.7b and baseline of 17.2b

bsearch153.0ms

Steps
ItersRangePoint
7
1.0287602518645422e+130
2.1844553541186674e+131
2.142771060817918e+130
6
3.3205719084428313e-53
5.076196012337531e-52
4.025640998297273e-53
11
1.439052447375511e-142
6.910766375266431e-122
1.0461098657879155e-126
10
-3.0087443311191178e+113
-8.941092352424513e+102
-2.50956257524698e+113

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03728
13828
23828

end0.0ms

sample527.0ms

Algorithm
intervals
Results
309.0ms8514×body80valid